Numerical Applications - Class 11 Commerce Applied Mathematics - Extra Questions
A machine in a soft drink factory fills $$840$$ bottles in six hours. How many bottles will it fill in five hours ?
Meena, Neena and Raveena can knit a shawl in 6, 4 and 8 hours respectively. What portion of the shawl will they knit in 1 hours. If they work together ?
Ramesh alone can harvest a field in $$16$$ days. Sohan and Ramesh both working together can harvest the field in $$12$$ days. They work together for $$8$$ days and then Ramesh leaves. In how many days will Sohan harvest the remaining field ?
12 persons can dig 324 cubic meters earth in a day. How many person will be required to dig 270 cubic meters earth ?
At what time between 3 O'Clock and 4 O'Clock will the two hands coincide ?
Two taps A and B fill an overhead water tank in 12 hours and 8 hours respectively. If both of them are opened together, how long would they take to fill the tank completely?
A can do a certain work in 12 days, B in 18 days and C in 24 days. A and B work together for 3 days and then A leaves the remaining work is done by B and C. How long did B and C take to complete the work ?
Tinku pours $$10^5$$ granules of sand per second in a bottle and it takes him 320 seconds to fill it. How much time will he take to fill that bottle if he pours 106 granules per second ?
A garrison of 300 men had food for 20 days. However 50 men leave. How many days the food will last now ?
1000 soldiers in a fort had enough food for 20 days. But some soldiers were transferred to another fort and the food lasted for 25 days. How many soldiers were transferred ?
If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
Three friends, Shalini, Manju and Rekha, had their birthdays as follows
Shalini was born on $$\text{2 September}$$ and it was a Wednesday. Rekha was born on $$\text{26 June}$$ of the same year. Manju's birthday is exactly in the middle of Shalini's and Rekha's birthday.
On which day was Manju born ?
It was $$6th$$ of a month on Wednesday. What date would it be $$5$$ days after Friday in the next to next week ?
Ashok remembers that his sister Asha's birthday is after 19 April and before 22 April, whereas his mother remembers Asha's birthday to be after 20 April but before 24 April. Based on this, when did Asha's birthday fall?
25 men were employed to do a piece of work in 24 days After 15 days 10 more men were engaged and the work was finished a day too soon In what time could they finish the work if extra men were not employed
The day after tomorrow is Pooja. The same day in the next week falls the Diwali. Today is Monday. What will be the day on day after Diwali ?
Soumya was born on $$\text{30 January 1984}$$, and her cousin Sundeep was born on the $$40th$$ day after the day of her birth. On which date was Sundeep born ?
It was Thursday on $$\text{1 October 1981}$$. On which date was it, $$4$$ days prior to the fifth Sunday immediately after $$\text{1 October}$$, and which day was it ?
$$A$$ and $$B$$ undertake to do a piece of work for $$Rs. 600$$. $$A$$ alone can do it in $$6$$ days while $$B$$ alone can do it in $$8$$ days. With the help of $$C$$ they finish it in $$3$$ days. Find $$B$$'s share.
A pipe can empty the tank in $$8$$ hours and another can fill $$6$$ liters in $$ 1$$ min. If both pipe opened , the tank is emptied in $$12$$ hours . The capacity of tank is ?
What time should last watch show?
What should the minute hand point to on the bottom clock?
Where should the missing hour hand point to on the bottom clock?
Where should the minute hand point on to the bottom clock?
Where should the minute hand point to on the bottom clock?
What time should the missing hand point to on the bottom clock?
Where should the missing hand point to?
A is twice more efficient than B and he can complete the work $$12$$ days carlier than B. In what time can B complete the work?
Tap $$A$$ can fill a tank in $$8$$ hours while tap $$B$$ can fill it in $$4$$ hours. In how much time will the tank be filled if both $$A$$ and $$B$$ are opened together?
Consider that the base of a square pyramid is equal to the length of side of cube. Then $$\dfrac{\text{Volume of Cube}}{\text{Volume of Square Pyramid}} = $$
There are two pipes $$A$$ and $$B$$ connected to a tank. It is known that $$A$$ can fill the tank in $$4$$ hours while $$B$$ can empty the tank in $$6$$ hours. If both the pipes are opened together, how much time will it take to fill up the tank?
Suppose $$A$$ alone can finish a piece of work in $$15$$ days and $$B$$ alone can do it in $$20$$ days. If both of them together, how much time will they take to finish it?
A tank can be filled by pipe $$p_1$$ in 3 hours and by pipe $$P_2$$ in $$5$$ hours. When the tank is full, it can be drained by pipe $$P_3$$ in $$4$$ hours. If the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?
If $$7$$ pipes can fill a take in $$1$$ hour $$24$$ minutes, how long will it take to fill the tank if $$6$$ pipes of the same type are used?
Find the volume of the following triangular pyramid whose base is triangle with side of 18 cm and and altitude of 17 cm and height of pyramid is 23 cm?
$$OA, OB, OC$$ are there mutually perpendicular straight lines in space. If $$\overline{OA} = a, \overline{OB} = b$$, and $$\overline{OC} = c$$, then the volume of the pyramid $$OABC$$ is $$\dfrac{abc}k$$. Find the value of $$k$$.
The volume of right triangular prism $$=$$ area of base $$\times $$ height
$$\dfrac { abc }{ k } =\dfrac { 1 }{ 2 } \times c\times b\times a$$
$$\dfrac { abc }{ k } =\dfrac { abc }{ 2 } $$
$$\therefore $$ $$k = 2$$
Rainfall of a place in a week is $$4\ cm, 5\ cm, 12\ cm, 3\ cm, 6\ cm, 8\ cm, 0.5\ cm$$. Find the average rainfall per day
The area of the base of a square pyramid is $$18\ cm^2$$ and the height is $$5\ cm$$. Calculate the volume of the pyramid (in $$cm^2$$).
If the mean of $$10, 12, 18, 13, P$$ and $$17$$ is $$15$$, find the value of P
A pyramid with trapezium base with sides $$AB=9\ cm, BC=12\ cm, CD=15\ cm$$, and $$DA=18\ cm$$. The volume of pyramid $$= 1458\ {cm}^3$$. Find the height, $$H$$, in cm?
In a trapezium $$ABCD$$,
$$\triangle ABC=90^{o}$$ and $$ADC$$ is a scalene triangle
In triangle $$ABC$$,
Area of $$ABC=\dfrac{1}{2}\times AB \times BC$$
$$=\dfrac{1}{2}\times 12 \times 9=54\ cm^2$$
In triangle $$ADC$$,
Semi-perimeter $$=S=(AC+AD+CD)/2=\dfrac{15+18+15}{2}=24\ cm$$
Area of $$\triangle ADC=\sqrt{s(s-a)(s-b)(s-c)}$$
$$=\sqrt{24(9)(9)(6)}=6\times 2\times 9=108\ cm^2$$
$$\therefore$$ Area of trapezium $$ABCD=A(\triangle ABC) + A(\triangle ACD)=108+54=162\ cm^2$$
Volume of pyramid $$=\dfrac{1}{3}$$Area of trapezium $$\times $$ height
$$=\dfrac{1}{3}\times 162\times h$$
$$\therefore\ h=27\ cm$$.
Hence, the answer is $$27$$.
Time spent by a student in a day is shown in the figure. Find how much time is spent in
(i) school
(ii) play ground
(iii) other activities
The sum of $$15$$ observations of a data is $$420$$. Find the Mean
Find the mean of the following data:
$$5,6,9,10,6,12,3,6,11,10$$.
A, B, and C are employed to do a piece of work for Rs. $$600$$. A and C are supposed to finish $$\dfrac { 5 }{ 6 }$$ of the work together. How much shall be paid to B?
$$ A+B +C = 600 \,Rs $$
$$ A+C = \dfrac{5}{6}$$ (total work)
$$ B = \dfrac{1}{6}$$ (total work)
$$ B = \dfrac{1}{6} \times 600 $$
$$ \boxed{B = 100 \, Rs }$$
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Choose the correct answer from the alternative given.
A and B can together finish a work in $$30$$ days. They worked at it for $$20$$ days and then B left The remaining work was done by A alone in $$20$$ more days. A alone can finish the work in
$$B$$ took $$16$$ days less than $$A$$ to do a piece of work. If both work together, they finish the work in $$15$$ days. How much time will $$B$$ alone takes to do the same work.
Ashok's school timing is form$$9:30\ h$$ to $$15:30\ h$$. Write his school timing in the $$12-h$$ clock.
..........................
$$8$$ men and $$12$$ boys can finish a piece of work in $$10$$ days while $$6$$ men and $$8$$ boys can finish in it $$14$$ days. Find the time taken by $$1$$ man alone and that by one boy alone to finish the work.
Two taps can fill a cistern in 10 hours and 8 hours respectively. A third tap can empty it in 15 hours. Now long will it take to fill the empty cistern, if all of them are opened together?
Three friends went to a hotel and had breakfast to their taste, paying $$Rs.16, Rs.17$$ and $$Rs.\ 21$$ respectively
(i) Find their mean expenditure.(ii) If they have spent $$3$$ times the amount that they have already spent, what would their mean expenditure be?
(iii) If the hotel manager offers $$50%$$ discount, what would their mean expenditure be?
(iv) Do you notice any relationship between the change in expenditure and the change in mean expenditure?
Find the mean of each of the data. $$\dfrac{1}{{3}},\,\,\,\dfrac{3}{{4}},\,\,\dfrac{5}{{6}},\,\,\dfrac{1}{{2}},\,\,\dfrac{7}{{12}}$$
Find the mean of the $$4,3,3,5,4,5,4$$.
A tap can fill a tank in 24 hours and an outlet can empty the full tank in 30 hours. In how many hours the empty tank will be filled, if both the tap and the outlet are opened simultaneously ?
Runs scored by ten batsman in one day cricket match are given. Find the average runs scored
$$23,54,08,94,60,18,29,44,05,86$$
The age of $$5$$ boys are $$8, 9, 11$$ and $$10$$ years. Calculate the average age?
Find the arithmetic mean of the sales per day in a fair price shop in a week. $$Rs. 10,000, Rs, 10,250, Rs. 10,790, Rs, 15,350, Rs. 10,110$$,
8 men complete a work in 6 hours.In how many hours many will 12 men complete the same work?
The mean $$x,x+3,x+6,x+9$$ and $$x+12$$ is
$$x,x+3,x+6,x+9,x+12$$
Mean $$=\dfrac{x+x+3+x+6+x+9+x+12}{5}$$
$$=\dfrac{5x+30}{50}=x+6$$
Pocket money $$(in )$$ received by $$7$$ students are $$ 78, 82, 76, 84, 80, 72, 74.$$ Find the range and also find the mean.
Solution -
Range = largest pocket money - smallest pocket money
$$ = 84-72 $$
$$ = 8 $$
Mean $$ = \frac{78+82+76+84+80+72+74}{7} $$
Mean $$ = 78 $$
Find the arithmetic mean of first five prime numbers.
$$70$$ patients in a hospital consume $$1350$$ liters of milk in $$30$$ days. At the same rate, how many patients will consume $$1710$$ liters of milk in $$20$$ days.
The distance between two places $$A$$ and $$B$$ on road is $$70$$ kilometers. A car starts from $$A$$ and the other from $$B$$. If they travel in the same direction, they will meet after $$7$$ hours. If they travel towards each other they will meet after $$1$$ hour, then find their speeds.
R.E.F.Image.
Time t
For (A)
$$ \frac{70+d}{t} = u_{A}$$
$$ \Rightarrow t = 7 hrs$$
$$ \therefore 70+d = 7u_{A}$$
For (B)
$$ \frac{d}{t}=u_{B}$$
$$ d = 7u_{B}$$
$$ d_{1}+d_{2} = 70 $$
$$ \Rightarrow u_{A}t+u_{B}t = 70$$
$$ \Rightarrow u_{A}+u_{B}=70$$ __(1)
Hence, $$ 70+7u_{B} = u_{A}$$
$$ \Rightarrow u_{A} = u_{B}+10$$ __ (2)
solving $$eq^{ns}$$ (1) & (2)
$$ u_{B} = 30 km/hr$$
$$ u_{A} = 10 km/hr$$
Rupali takes 15 days to complete embroidery work in a saree Find her rate of work done .
A tanl can be filed by 5 pipes in 80 minutes. How long it will take to fill the tank by 8 pipes of same size?
$$10$$ men can lay a road $$75\ km$$. long in $$5$$ days In how many days can $$15$$ men lay a road $$45\ km$$. long
Nimesh completes his work in $$20$$ minutes. Find his rate of work done.
A Cricket player scored $$180$$ runs in the first match and $$257$$ runs in the second match. Find the number of runs he should score in the third match so that the average of runs in the three matches be $$230$$.
A person on tour has Rs. 4200 for his expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by Rs.Find the original duration of the tour.
A can do a piece of work in 80 days.He works at it for 10 days and then B alone finishes remaining work in 42 days. In how many days could both do it?
Now A can do a price of work in $$80$$ days. So let the total work $$=80$$units.
$$A\rightarrow 80$$ days$$=1$$ unit/day
So in $$10$$ days, A has completed $$10$$ units
$$\therefore$$ Remaining work$$=70$$ units
Now B finishes this in $$42$$ days. So rate of work if $$B=\dfrac{70}{42}=\dfrac{5}{3}$$ unit/day
Thus$$=A+B=1+\dfrac{5}{3}$$
$$=\dfrac{8}{3}$$
So time taken$$=\dfrac{\dfrac{80}{8}}{3}=30$$days.
A water pipe can fill half of the water tank in $$45$$ minutes. How much time will it take to fill $$4$$ such water tanks?
A boy riding a bicycle covers a distance of $$10$$ m in $$40$$ s. What is the speed of the boy?
The mean of 2,3,5,7,8, is
Find the mean of the following data $$5,6,9,10,6,12,36,11,10$$
X can do a piece of work in 25 days and Y can finish it in 20 days. They work together for 5 days and then X leaves. In how many days will Y finish the remaining work ?
$$A, B$$ and $$C$$ can do a piece of work in $$15, 12$$ and $$20$$ days respectively. They started the work together, but $$C$$ left after $$2$$ days. In how many days will the remaining work be competed by $$A$$ and $$B$$?
Rice costing $$Rs.\ 960$$ is needed for $$16$$ members for $$40$$ days. What is the cost of rice required for $$24$$ members for $$15$$ days.
Change the following :
8 minutes to seconds
Three persons can build a small house in 8 days. To build the same house in 6 days, how many persons are required?
The heights of students are $$152,148,160,142,148$$. Find mean.
The mean of $$34,78,12,89,45 $$ is
Find the mean of $$21,30,50,60,20,19$$
The mean of $$62,76,45,98,77,84$$
The mean of $$65,24,81,35,79$$
The mean of $$12,23,34,45,56,67,78,89,90$$ is
Two pipes A and B can fill a tank in 20 and 16 hours respectively. Pipe B alone is kept open for 1/4 of time and both pipes are kept open for remaining time. In how many hours, the tank will be full?
A submarine is at sea level. At 8.00 p. m it begins to descend at a rate of 8 m per minute. At what time will it be at - 240 m ?
8 meter $$\rightarrow $$ 1 min
240 meters $$\rightarrow $$ x mins
$$x=\frac{240}{8}=30$$ mins
so 8.30 pm
The mean of $$22,54,35,13,12$$ is __________.
Find the mean of :
$$3, 1, 5, 4, 4$$ and $$7$$
A person has earned his income during the financial year 2017-18 then write assessment year.
A car travels 60 km in 45 minutes. Find its speed in km/h ?
In 8 minutes, rajan jogs 800 metres. What is this speed in km/h?
Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it?
Sahil takes $$3\frac{1}{5}$$ minutes to walk across the park. Rohan takes $$\frac{{10}}{3}$$ minutes to do the same. who take less than and by what fraction ?
The mean of $$16,12,8,p,11,10$$ and $$9$$ is $$12 $$. Find the value of '$$p$$'.
Mean $$ = \frac{16+12+8+P+11+10+9}{7}$$
$$ 12= \frac{16+12+8+P+11+10+9}{7}$$
$$ 12\times 7 = P + 66 $$
$$ P = P + 66 $$
$$ P = 84-66 $$
$$ P = 18 $$
$$A, B$$ and $$C$$ can do a piece of work in $$10$$ days, $$12$$ days and $$15$$ days respectively. How long will they take to finish it if they work together?
$$A$$ can do a piece of work in $$24$$ hours while $$B$$ alone can do it in $$16$$ hours. If $$A, B$$ and $$C$$ working together can finish it in $$8$$ hours, in how many hours can $$C$$ alone finish the work?
The mean of $$42,58,61,47,53$$ is
The mean of $$7,3,9,6,8$$ is
Find the average of first 5 odd numbers.
$$A, B$$ and $$C$$ working together can finish a piece of work in $$8$$ hours. A alone can do it in $$20$$ hours and $$B$$ alone can do it in $$24$$ hours. In how many hours will $$C$$ alone do the same work?
$$A$$ and $$B$$ can finish a piece of work in $$16$$ days respectively. $$A$$ started the work and worked at it for $$2$$ days. He was then joined by $$B$$. Find the total time taken to finish the work.
Find the mean of the following distribution:
| $$x$$ | $$4$$ | $$6$$ | $$9$$ | $$10$$ | $$15$$ |
| $$f$$ | $$5$$ | $$10$$ | $$10$$ | $$7$$ | $$8$$ |
The amount donated by some households in their religious organisation are as follows.
| Amount (in $$Rs$$) | Number of households |
| Less than $$100$$ | $$14$$ |
| Less than $$200$$ | $$22$$ |
| Less than $$300$$ | $$37$$ |
| Less than $$400$$ | $$58$$ |
| Less than $$500$$ | $$67$$ |
| Less than $$600$$ | $$75$$ |
What values do these households possess?
The table below gives the distribution of villages under different height from sea level in a certain region.
| Height in meters | $$200$$ | $$600$$ | $$1000$$ | $$1400$$ | $$1800$$ | $$2200$$ |
| No. of villages | $$142$$ | $$265$$ | $$560$$ | $$271$$ | $$89$$ | $$16$$ |
| No. of children | $$0$$ | $$1$$ | $$2$$ | $$3$$ | $$4$$ | $$5$$ |
| No. of families | $$5$$ | $$11$$ | $$25$$ | $$12$$ | $$5$$ | $$2$$ |
$$A$$ can do a piece of work in $$14$$ days while $$B$$ can do it in $$21$$ days. They began together and worked at it for $$6$$ days. Then , $$A$$ fell and $$B$$ had to complete the remaining work alone. In how many days was the work completed?
| No. of children | $$0$$ | $$1$$ | $$2$$ | $$3$$ | $$4$$ | $$5$$ |
| No. of families | $$5$$ | $$11$$ | $$25$$ | $$12$$ | $$5$$ | $$2$$ |
The monthly salaries in rupees of $$30$$ workers in a factory are given below.$$5000, 7000, 3000, 4000, 4000, 3000, 3000, 3000, 8000, 4000, 4000, 9000, 3000, 5000, 5000, 4000, 4000, 3000, 5000, 5000, 6000, 8000, 3000, 3000, 6000, 7000, 7000, 6000, 6000, 4000$$.From the above data find the mean of monthly salary.
$$A$$ and $$B$$ can do a work in 8 days. $$B$$ and $$C$$ together in 6 days while $$C$$ and $$A$$ together in 10 days. If they all work together, in The work will be completed in $$\dfrac {k}{17}$$ days, where $$k$$ is
Two pipes $$A$$ and $$B$$ can fill a cistern in 20 minutes and 25 minutes respectively. Both are opened together but at the end of 5 minutes $$B$$ is turned off. What is the total time taken to fill the cistern?
If $$52$$ men can do a piece of work in $$35$$ days, in how many days $$28$$ men will do it ?
If $$5$$ men or $$7$$ women can earn Rs. $$875$$ per day, how much would $$10 $$ men and $$5$$ women earn per day ?
A, B and C can do a piece of work 6, 8 and 12 days respectively B and C work together for 2 days then A takes C's place How long will it take to finish the work
If the day that dawned two days preceding the day before yesterday was Sunday, what day of the week will dawn $$2$$ days following the day after tomorrow ?
Monday dawned on the day preceding $$3$$ days before day before yesterday. What day will dawn $$2$$ days after tomorrow ?
Mahesh was born on $$\text{11 August 2004}$$. His younger sister Malini was born exactly after $$100$$ weeks. What is the date of birth of Malini ?
If the day that will dawn two days after tomorrow is Monday, what day of the week had dawned two days before the day before yesterday?
Between $$1$$ o'clock and $$2$$ o'clock, find the time when the minute hand and an hour hand are coinciding.
A batsman scored the following number of runs in six innings-
$$36, 35, 50, 46, 60, 55$$
Calculate the mean runs scored by him in an inning
$$A, B$$ and $$C$$ can do a piece of work in $$6, 8$$ and $$12$$ days respectively. $$B$$ and $$C$$ work together for $$2$$ days, then $$A$$ takes $$C$$'s place. How long will it take to finish the work?
$$A$$ and $$B$$ can separately do a piece of work in $$20$$ and $$15$$ days respectively. They worked together for $$6$$ days after which $$B$$ was replaced by $$C$$. If the work was finished in next $$4$$ days, then the number of days in which C alone could do the work will be
Two pipes $$M$$ & $$N$$ can fill a cistern in $$12$$ & $$16$$ hrs respectively. If both the pipes are opened together, then after how many minutes $$N$$ should be closed so that the tank is full in $$9$$ hrs.
If $$12$$ men or $$18$$ women can reap a field in $$7$$ days, in how many days can $$4$$ men & $$8$$ women reap the same field?
Twenty-two women together can complete a work in $$16$$ days, $$16 $$ men together can complete the same work in $$15$$ days. What is the ratio of the working capacity of a man to that of a woman?
A teacher wants to make a test containing $$20$$ verbal and $$30$$ math questions. Each verbal question is to be allotted $$45$$ seconds to complete and each math question is to be given $$1$$ minute $$20$$ seconds. How many minutes should she allow for the whole test?
If $$7$$ men or $$9$$ women can do a piece of work in $$32$$ days, in what time $$7$$ men and $$9$$ women will complete $$\dfrac 12$$ of the work?
$$15$$ men can do a piece of work in $$24$$ days. In what time $$10$$ men can complete $$\dfrac{1}{3}$$ of the work.
A can complete a piece of work in $$14$$ days. He worked for $$2$$ days and remaining work was completed by B in $$12$$ days. If they start the work together, then in what time they can complete the work?
A tank is in the shape of a square based pyramid. The base is $$3$$m and height is $$2.5$$m. Find the capacity of water in liters.
A port had provisions for $$450$$ men for $$80$$ days. After$$ 10$$ days $$50$$ more men arrived. How long will the remaining food last at the same rate?
Suppose $$A$$ can do a piece of work in $$14$$ days while $$ B$$ can do it in $$21$$ days. They begin together and worked at it for $$6$$ days. Then $$A$$ fell ill and $$B$$ had to complete the work alone. In how many days was the work completed?
Suppose $$A$$ and $$B$$ together can do a job in $$12$$ days, while $$B$$ alone can finish it in $$30$$ days. In how many days can $$A$$ alone finish the work?
Suppose three friends Rama, Rahim and John can paint a fence in $$2$$ hours. If Rama does it alone, he takes $$5$$ hours while Rahim alone takes $$6$$ hours. How long John takes to finish the job alone?
Suppose $$B$$ is $$60\%$$ more efficient than $$A$$. If $$A$$ can finish a job in $$15$$ days, how many days $$B$$ needs to finish the same job?
Suppose $$A$$ takes twice as much time as $$B$$ and thrice as much time as $$C$$ to complete a work. If all of them work together, they can finish the work in $$2$$ days. How much time $$B$$ and $$C$$ working together to finish it?
Find the volume of a square pyramid if the area of its base is $$150$$ $$cm^2$$ and height is $$9$$cm.
If $$36$$ men can build a wall of $$140\ m$$ long in $$21\ days$$, how many men are required to build a similar wall of length $$50\ m$$ in $$18\ days$$?
Suppose $$A$$ is twice as good a workman as $$B$$ and together they can finish a job in $$24$$ days. How many days $$A$$ alone takes to finish the job?
A pipe can fill a cistern in $$9$$ hours. Due to a leak in its bottom, the cistern fills up in $$10$$ hours. If the cistern is full, in how much time(in hours) will it be emptied by the leak?
If the cost of $$65$$ tea-packets of the same size is Rs.$$2600$$, what is the cost of $$75$$ such packets?
The base of a right pyramid is a regular hexagon whose area is $$243$$ square cm. If the area of a side face the pyramid is $$46$$ square cm, what should be its volume (in cc.) in the nearest interger value?
The base of right pyramid, $$h$$ cm height is a square. It is divided into two parts by a plane parallel to the base so that volumes of the two parts are equal. If the distance of the plane form the vertex is $$\dfrac h{\sqrt[a] b}$$ cm, then find the value of $$(a-b)^2$$.
Volume of square base pyramid$$=\cfrac { 1 }{ 3 } \times { B }_{ A }\times h$$
$${ B }_{ A }=$$Area of base
(Image)
By symmetry,
$$\cfrac { { h }^{ 1 } }{ h } =\cfrac { { l }^{ 1 } }{ l } $$
Acc. to question,
$$\cfrac { 1 }{ 3 } { B }_{ a }\times h=\left( \cfrac { 1 }{ 3 } \times { B }_{ a }^{ 1 }\times { h }^{ 1 } \right) \times 2$$
$$\Rightarrow \cfrac { 1 }{ 3 } \times { l }^{ 2 }h=\cfrac { 2 }{ 3 } { \left( { l }^{ 1 } \right) }^{ 2 }{ h }^{ 1 }$$
$$\Rightarrow \cfrac { 1 }{ 2 } ={ \left( \cfrac { { l }^{ 1 } }{ l } \right) }^{ 2 }\times \cfrac { { h }^{ 1 } }{ h } $$
$$\left( \cfrac { { h }^{ 1 } }{ h } \right)^{ 3 }=\cfrac { 1 }{ 2 } $$
$${ h }^{ 1 }=\cfrac { h }{ \sqrt [ 3 ]{ 2 } } $$
$$a=3$$
$$b=2$$
$${ \left( a-b \right) }^{ 2 }={ 1 }^{ 2 }=1$$
$$A$$ and $$B$$ together can finish a piece of work in $$12$$ days. If '$$A$$' alone can finish the same work in $$20$$ days, in how many days $$B$$ alone can finish it?
Find the mean of first $$n$$ natural numbers.
What is the height of a square pyramid of base edge $$12cm$$ and slant height $$10cm$$? Find its volume.
For a square pyramid
Base edge $$=s=12cm$$
Slant height $$=l=10cm$$
Since the base of the pyramid is square,
Therefore, $$a=\cfrac { diagonal }{ 2 } $$
Diagonal of square of base $$12\sqrt{2}cm$$
$$a=6\sqrt{2}cm$$
$$h=\sqrt { { 10 }^{ 2 }-{ a }^{ 2 } } =\sqrt { { 10 }^{ 2 }-{ 6\sqrt { 2 } }^{ 2 } } =\sqrt { 100-72 } =\sqrt { 18 } =3\sqrt { 2 } cm$$
Volume$$=\cfrac { 1 }{ 3 } { s }^{ 2 }h=\cfrac { 1 }{ 3 } \times 18\times 8=144\sqrt2{ cm }^{ 3 }$$
Base edge $$=s=12cm$$
Slant height $$=l=10cm$$
Since the base of the pyramid is square,
Therefore, $$a=\cfrac { diagonal }{ 2 } $$
Diagonal of square of base $$12\sqrt{2}cm$$
$$a=6\sqrt{2}cm$$
$$h=\sqrt { { 10 }^{ 2 }-{ a }^{ 2 } } =\sqrt { { 10 }^{ 2 }-{ 6\sqrt { 2 } }^{ 2 } } =\sqrt { 100-72 } =\sqrt { 18 } =3\sqrt { 2 } cm$$
Volume$$=\cfrac { 1 }{ 3 } { s }^{ 2 }h=\cfrac { 1 }{ 3 } \times 18\times 8=144\sqrt2{ cm }^{ 3 }$$
The number of passengers who travelled in APSRTC bus from Adilabad to Nirmal in $$4$$ trips in a day are $$39, 30, 45$$ and $$54$$. What is the occupancy ratio (average number of passengers travelling per trip) of the bus for the day?
If two pipes function simultaneously, the reservoir will be filled in $$12$$ hours. Through one pipe the reservoir is filled up $$10$$ hours faster than through the other. How many hours does it take the second pipe to fill the reservoir?
Two workers, working together, completed the job in $$5$$ days. If one worker worked twice as fast and the other worked half as fast, they would have to work for $$4$$ days. How much time would it take the first worker to do the job if he worked alone.?
$$3$$ pumps who works $$8$$ hours per day empty the tank in $$2$$ days. How many hours per day will $$4$$ pumps use to empty the tank in $$1$$ day?
2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?
If 3 men or 4 women can earn Rs.960 in a day, how much would 6 men and 11 women earn in a day?
Some workers make 48 pots in 4day working 4 hour a day . If they work 5 hour everyday , in how many days can they make 90 pots ?
Neena, Meena and Tina can do a piece of work in 4 days, 8 days and 6 days respectively. Neena and Tina work together for 1 day and then Neena leaves and Tina is joined by Meena to complete the work. How long does Tina work(in hours)?
A tap can fill a tank in 24 hours and an outlet can empty the full tank in 30 hours. In how many hours the empty tank will be filled, if both the tap and the outlet are opened simultaneously?
If $$5$$ men or $$7$$ women can earn Rs. $$1575$$ in a day, how much would $$10$$ men and $$13$$ women earn in $$2$$ days?
The average salary of nine workers in a factory is Rs. 28000 per month. If the salary of the manager is Rs 50000 per month, find the average salary paid to all the employees.
The train travels $$360\ km$$ at a uniform speed if the speed has been $$5\ km/hr$$ more, it would have taken $$1$$ hour less for the same journey. Find the speed of the train.
A variable takes the values $$0, 1, 2, 3,.... n$$ with frequencies $$^nc_0, {^nc}_1, {^nc}_2, {^nc}_3, ...... {^nc}_n$$ the mean $$\bar{x} =$$
A regular square pyramid is $$3\ m$$. height and the perimeter of its base is $$16\ m$$. Find the volume of the pyramid.
$$5$$ women and $$2$$ men together can finish an embroidary work in $$4$$ days while $$6$$ women and $$3$$ men can finish it in $$3$$ days. Find the time taken by $$1$$ women alone to finish the work. Also find the time taken by $$1$$ man alone to finish the work.
A can dig a trench in $$6$$ days while B can dig it in $$8$$ days. They dug the trench working together and received Rs. $$1120$$ for it. Find the share of each in it.
| Subjects | English | Hindi | Maths | Science | Social Science |
| Marks | 67 | 76 | 88 | 85 | 78 |
(ii) Find the average marks.
(iii) In which subject the student has scored highest marks?
(iv) In which subject the student has scored lowest marks?
(v) What is the range of the marks obtained?
A.M. of the three quantities a + 2, a, a - 2, is ______
4 men and 6 woman can finish a work in 8 days while 3 mens and 7 womans can do that same work in 10 days.In how many days will 10 woman do the same work.
A can do a piece of work in 20 days, while B can do it in 15 days, with the help of C, they finished the work in 5 days. In what time would C alone do it?
A can mow a field in $$9$$ days; B can mow it in $$12$$ days while C can mow it in $$8$$ days. They all together mowed the field and received Rs. $$1610$$ for it. How will the money be shared by them?
Ten men working for $$6$$ days can complete $$5$$ copies of a books. If there are $$8$$ men working to complete $$4$$ copies of the books, how many days it will take?
given
$$\rightarrow $$ 10 men working for 6 dyas can complete
5 copies of a book
$$\rightarrow $$ number of copies filled by 10 members in 1 day
is 1/6
$$\rightarrow $$ work done by 10 numbers on one book is $$1/5$$
$$\rightarrow $$ if 8 men work for 4 copies in x days then
$$\rightarrow $$ work done on one book per one days is
$$\frac{1}{8}\times \frac{1}{4}\times \frac{1}{x}$$
but work done on one book by one person
is same
so, $$\frac{x}{32}=\frac{1}{300}$$
$$x= 9.375$$ days
Five workers take $$12$$ days to weed a field. How many days would $$6$$ workers take? How many would $$15$$ take
If the mean of $$20,24,36,26,34$$ and $$K$$ is $$30$$ then find $$K$$ .
Two pipes running together can fill a cistern in $$2\dfrac{8}{11}$$ minutes.If one pipe takes 1 minute more than the other to fill the cistern, find the time in which each pipe would fill the cistern alone.
The water acidity in a pool is considered normal when the average pH reading of three daily measurement is between $$7.2$$ and $$7.8$$.If the first two pH reading are $$7.48$$ and $$7.85$$, find the range of pH value for the third reading that will result in the acidity level being normal ?
Seema obtained the following scores (out of $$100$$) on a set of spelling tests: $$80,85,90,71,60,100$$. What is her mean score?
125 people can finish a piece of work in 120 days , find the no. of people required to finish this same work in 100 days .
A carpenter was hired to build 192 window frames . the first day he made five frames and each day thereafter he made two more frames than he made the day before. how many days did it take him to finish the job?
If 56 men can do a piece of work in 42 days, then in how many days will 48 men complete the same work ?
Pipe A can fill an empty tank in $$5$$ hours while pipe B can empty the fill tank in $$6$$ hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up completely?
If the mean of $$20,24,36,26,34$$ and $$K$$ is $$30$$ then find $$ K $$
$$A$$ alone can do a piece of work in $$12$$ days and $$B$$ alone can do the same work in $$16$$ days. They worked together on it for $$3$$ days and then $$A$$ left. How long did $$B$$ take to finish the remaining work?
If $$36$$ men can do a piece of work in $$25$$ days, in how many days will $$15$$ men complete the same work?
If $$7$$ women and $$5$$ men earns $$Rs\ 875$$ in a day, how much will $$5$$ women and $$10$$ men earn in one day?
If 4 workers can make 42 toys in 6 days. How many toys can 12 workers make in 3 days.
The table shows the points of each player scored in four games.
Players Game I Game II Game III Game IV X 14 16 10 10 Y 0 8 6 4 Z 8 11 Did not play 13
Determine $$X$$'s average number of points scored per game
| Players | Game I | Game II | Game III | Game IV |
| X | 14 | 16 | 10 | 10 |
| Y | 0 | 8 | 6 | 4 |
| Z | 8 | 11 | Did not play | 13 |
A workforce of $$50$$ men with a contractor can finish a piece of work in $$5$$ months. In how many months the same work can be completed by $$125$$ men
To produce given number of water pouches machine $$A$$ takes $$20$$ hours and machine $$B$$ takes $$30$$ hours. If both the machine are operated simultaneously in what time will the given number of a pouches can be produced.
A garrison of $$200$$ men had provisions for $$45$$ days. After $$15$$ days, $$40$$ more men join the garrison. Find the number of days for which the remaining food will last
$$30$$ men can finish a piece of work in $$28$$ days.How many days will be taken by $$21$$ men to finish it?
4 men and 6 boys can finish a piece of work in 5 days while 3 men and 4 boys can finish it in 7 days. Find the time taken by 1 man alone or than by 1 boy alone.
An employee works in a company on a contract of $$30$$ days on the condition that he will receive Rs. $$200$$ for each day he works and he will be fined Rs. $$20$$ for each day he is absent. If he receives Rs. $$3800$$ in all, for how many days did he remain absent?
$$A, B$$ and $$C$$ are employed to do a piece of work for $$Rs.529.$$ $$ A$$ and $$B$$ together are supposed to do $$\dfrac { 19 } { 23 }$$ of the work and $$B$$ and $$C$$ together $$\dfrac { 8 } { 23 }$$ of the work. What amount should $$A$$ be paid ?
There are $$800$$ soldiers in an army camp. There is enough provisions for them for $$60$$ days. If $$400$$ more soldiers join the camp, for how many days will the provisions last?
If $$20$$ men working together can finish a job in $$20$$ days, then find the number of day taken by $$25$$ men of the same capacity to finish job.
A and B can polish a floor of a building in 18 days. A alone can do $$\frac {1}{6}$$ of this job in 4 days. In how many days can B alone polish the floor?
Rate of A to polish the floor is x sq unit/ day
Rate of B to polish the floor is y sq unit/ day
Let total area of floor = W sq. unit
W= $$(x+y)\times 18$$ _________ (i) [When both work together]
$$\frac{W}{6}=x\times 4$$ [When A alone do $$\frac{W}{6}$$ job
$$\Rightarrow W=24x$$ _____(ii) in 4 days]
Let B alone do the complete job in t days
$$W=y\times t$$ _____ (iii)
From equation (i) & (ii)
$$W=(\frac{W}{24}+y)\times 18\Rightarrow y=\frac{w}{18}-\frac{w}{24}=\frac{w}{72}$$ _______ (iv)
Equation (iii) $$\Rightarrow W=y\times t=\frac{w}{72}\times t$$
$$\Rightarrow t= 72$$ days
Rahul left the school at 6:40 am and reached school at 7:20 am. How long did he take reach school?
A can do a price of work in 6 hours white B can do it in 8 hours. With the help of C, they completed the work in $$2\frac{1}{2}$$ hours. In what time can C alone complete the work?
A car travel $$90 km$$ in $$2.5$$ hours, How much time is required to cover $$60 km$$ with the same speed?
find the distance covered in $$4$$ hours?
$$90$$km $$\rightarrow 2.5$$hrs.
Speed$$=\dfrac{90}{2.5}=36$$ km/hr
i) Time required $$=\dfrac{60}{36}=\dfrac{5}{3}$$ hrs
Distance covered$$=36\times 4=144$$km.
$$A$$ and $$B$$ can do a piece of work in $$10$$ days. $$B$$ and $$C$$ can do it in $$12$$ days. $$A$$ and $$C$$ can do it in $$15$$ days. How long will $$A$$ take to do it alone?
Find the mean of the first ten prime numbers.
$$175$$ men can dig a canal $$3150\ m$$ long $$36$$ days. How many men are required to dig a canal $$3900\ m$$ long in $$24$$ days?
During $$5$$ successive hours a car covered $$65$$ km, $$72$$ km, $$68$$ km, $$70$$ km and $$55$$ km. Find average speed of the car per hour.
Calculate the mean of the following distributions:
| x | 8 | 12 | 15 | 20 | 25 | 30 |
| f | 10 | 5 | 20 | 8 | 4 | 3 |
$$A$$ can do a piece of work in $$12$$ days while $$B$$ can do it in $$8$$ days. With the help of $$C,$$ they finish the work in $$4$$ days. Then, $$C$$ alone can do the work in
Two cards are drawn simultaneously (or successively without replacement ) from a well shuffled pack of $$52$$ cards. Find the mean and variance of the number of red cards.
A man begins his journey from delhi to Jaipur by car. He covers a distance of $$120$$ km at a speed of $$60$$ km/h, next $$160$$ km at $$80$$ km/h.Calculate the average seed of the whole journey.
If $$6$$ men and $$8$$ boys can do a piece of work in $$10$$ days while $$26$$ men and $$48$$ boys can do the same in $$2$$ days the time taken by $$15$$ men and $$20$$ boys in doing the same type of work will be:
$$6$$ pipes can fill a tank in $$1$$ hour $$24$$ minutes. How long will it take to full the tank if $$7$$ pipes are used
A B and C can do a piece of work in $$20, 30$$ and $$60$$ days respectively. In how many days A can do the work if he is assisted by B and C on every third day?
A fast train covers $$360\ km$$ in $$3$$ hours $$20$$ minutes. How much time will it take to cover a distance of $$90\ km$$.
A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. How much time will A take to complete the remaining work alone?
An aircraft has 120 passenger seats. The number of seats occupied during 100 fights is given below :
| No. of seats | 100-104 | 104-108 | 108-112 | 112-116 | 116-120 |
| Frequency | 15 | 20 | 32 | 18 | 15 |
A labour earns Rs.1980 in 12 days.How much does he earns in 7 days.
$$A$$ alone can do a piece of work in $$15$$ days and $$B$$ alone can do the same work in $$12$$ days.$$A$$ works alone for the first four days. In how many days will $$A$$ and $$B$$ together finishing the remaining work?
The mean of $$20$$ numbers is $$20$$. If $$2$$ is added to each of the first ten numbers, find the mean of the new set of $$20$$ numbers.
Water is pouring into a cuboidal reservoir at the rate of 60 milliliters per minute. If the volume of the reservoir is 180 liters find the number of hours it will take to fill the reservoir.
The angle of elevation of a jet plane from a point A on the ground is $$60^{\circ}$$. After a flight of 15 seconds the angle of elevation changes to $$30^{\circ}$$. If the jet plane is flying at a constant height of 1500 $$\sqrt{3}$$, find the speed of the jet plane.
Find the average of numbers $$87, 84, 86, 90, 82, 88, 78$$.
What is the mean of $$1 ^ { \text { st } }$$ ten prime numbers?
Find the mean of $$7$$, $$10$$, $$4$$ and $$17$$
The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in Figure Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per $$cm^{2}$$ and black paint costs 5 paise per $$cm^{2}$$.
A wall of length $$10m$$ was to be built across an open ground. The height of the wall is $$4m$$ and thickness of the wall is $$24cm$$. If this wall is to be built up with bricks whose dimensions are $$24cm\times 12cm\times 8cm$$, how many bricks would be required?
The length of a hall is $$18m$$ and the width $$12m$$. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall in m.
If the heights of 5 persons are 140 cm, 150 cm, 152 cm, 158 cm and 161 cm respectively, find the mean height.
Find the mean of 994,996,998,1002 and 1000.
An aeroplane left 30 minutes later than its scheduled time and in order to reach its destination 1500 km away in time, it had to increse its speed by 250 km/hr from its usual speed. Determine its usual speed.
A mathematics lesson starts at $$11:05$$.
The lesson lasts for $$75$$ minutes.
Work out the time that the lesson ends.
The diagram shows a water container in the form of an inverted pyramid, which is such that when the height of the water level is $$h\, cm$$ the surface of the water is a square of side $$\dfrac{1}{2}h\,cm$$.
(i) Express the volume of water in the container in terms of $$h$$.
(ii) Water is steadily dripping into the container at a constant rate of $$20cm^3$$ per minute. Find the rate, in cm per minute, at which the water level is rising when the height of the water level is 10cm.
A worker paid $$Rs. 1110$$ for $$6$$ days. If this wages during a month are $$Rs. 4625$$, for how many days did he work?
A girl can finish a book in $$25$$ days if she reads $$18$$ pages of every day. How many days will she take to finish, if she she reads $$15$$ pages every day?
Compute the mean of the following data :
| Class | $$1-3$$ | $$3-5$$ | $$5-7$$ | $$7-9$$ |
| Frequency | $$12$$ | $$2$$ | $$27$$ | $$19$$ |
Reeta types $$40$$ words per minute and takes $$24$$ minutes to type a certain document. Her friend Geeta has a typing speed of $$48$$ words per minute. In how much time, will she be able to type the same document?
$$16$$ horses can consume a certain quantity of corn in $$25$$ days. In how many days would the same quantity be consumed by $$40$$ horses?
Height of students of Class $$X$$ are given in the following frequency distribution:
| Height (in cm) | $$150-155$$ | $$155-160$$ | $$160-165$$ | $$165-170$$ | $$170-175$$ |
| Number of students | $$15$$ | $$8$$ | $$20$$ | $$12$$ | $$5$$ |
Find the mean for the following distribution:
$$Mean=\Sigma fx/\Sigma f$$
$$=3757/60$$
$$=62.616$$
$$=62.62$$
Hence the mean is $$62.62$$
$$=3757/60$$
$$=62.616$$
$$=62.62$$
Hence the mean is $$62.62$$
Calculate the mean of the following distribution:
$$Mean=\Sigma f_ix_i/\Sigma f_i$$
$$=3600/100$$
$$=36$$
Hence the mean of the distribution is $$36$$
$$=3600/100$$
$$=36$$
Hence the mean of the distribution is $$36$$
Find the mean of the following distribution:
$$Mean=\Sigma f_ix_i/\Sigma f_i$$
$$=7150/50$$
$$=143$$
Hence the mean of the distribution is $$143$$
$$=7150/50$$
$$=143$$
Hence the mean of the distribution is $$143$$
Calculate the mean of the following distribution:
$$Mean=\Sigma fx/\Sigma f$$
$$=7420/80$$
$$=92.75$$
Henec the mean is $$92.75$$
$$=7420/80$$
$$=92.75$$
Henec the mean is $$92.75$$
The contents of $$100$$ matchboxes were checked to determine the number of matches they contained.
| No. of matches | 35 | 36 | 37 | 38 | 39 | 40 | 41 |
| No. of matchboxes | 6 | 10 | 12 | 15 | 11 | 7 | 8 |
$$Mean=\Sigma fx/\Sigma f$$
$$=3813/100$$
$$=38.13$$
Hence the mean is $$38.13.$$
$$=3813/100$$
$$=38.13$$
Hence the mean is $$38.13.$$
| Category | A | B | C | D | E | F | G |
| wages per day in(rs) | 50 | 60 | 70 | 80 | 90 | 100 | 110 |
| Number of workers | 2 | 4 | 8 | 12 | 10 | 6 | 8 |
The contents of $$100$$ matchboxes were checked to determine the number of matches they contained.
| No. of matches | 35 | 36 | 37 | 38 | 39 | 40 | 41 |
| No. of matchboxes | 6 | 10 | 12 | 15 | 11 | 7 | 8 |
bring the mean up to exactly $$39$$ matches. ($$1997$$)
New mean $$= 39$$
$$\Sigma fx = 39\times100 = 3900$$
So number of extra matches to be added $$= 3900-3813 = 87$$
Hence the number of extra matches to be added is $$87$$.
$$\Sigma fx = 39\times100 = 3900$$
So number of extra matches to be added $$= 3900-3813 = 87$$
Hence the number of extra matches to be added is $$87$$.
Find the mean of the following distribution.
$$Mean=\Sigma f_ix_i/\Sigma f_i$$
$$=985/41$$
$$=24.024$$
$$=24.02(approx)$$
Hence the mean of the distribution is $$24.02$$
$$=985/41$$
$$=24.024$$
$$=24.02(approx)$$
Hence the mean of the distribution is $$24.02$$
The table below gives the distribution of villages under different heights from sea level in a certain region.
| Height (in meters): | $$200$$ | $$600$$ | $$1000$$ | $$1400$$ | $$1800$$ | $$2200$$ |
| No. of village: | $$142$$ | $$265$$ | $$560$$ | $$271$$ | $$89$$ | $$16$$ |
The table below gives the distribution of villages under different heights from sea level in a certain region.
| Height (in meters): | $$200$$ | $$600$$ | $$1000$$ | $$1400$$ | $$1800$$ | $$2200$$ |
| No. of village: | $$142$$ | $$265$$ | $$560$$ | $$271$$ | $$89$$ | $$16$$ |
Find the mean of children per family from data given below:
| No. of children | $$0$$ | $$1$$ | $$2$$ | $$3$$ | $$4$$ | $$5$$ |
| No. of families | $$5$$ | $$11$$ | $$25$$ | $$12$$ | $$5$$ | $$2$$ |
Renu completed$$\dfrac{2}{3} $$ part of her homework in 2 hours. How many parts of her homework had she completed in $$1\dfrac{1}{4}$$ hours?
The following table gives the weekly wages (in Rs.) of workers in a factory :
Weekly wages (in Rs) | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 | 80-85 | 85-90 |
No. of workers | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |
Find the mean of the first five natural numbers.
The table below gives the distribution of villages under different heights from sea level in a certain region.
| Height (in meters): | $$200$$ | $$600$$ | $$1000$$ | $$1400$$ | $$1800$$ | $$2200$$ |
| No. of village: | $$142$$ | $$265$$ | $$560$$ | $$271$$ | $$89$$ | $$16$$ |
The table below gives the distribution of villages under different height from sea level in a certain region.
| Height in meters | $$200$$ | $$600$$ | $$1000$$ | $$1400$$ | $$1800$$ | $$2200$$ |
| No. of villages | $$142$$ | $$265$$ | $$560$$ | $$271$$ | $$89$$ | $$16$$ |
If $$5$$ men can do certain construction work in $$14$$ days, then how long will $$7$$ men take to complete the same construction work?
Enter 1 if it is true else enter 0.The mean of a data is defined as $$\dfrac{Sum \, of \, all\, observations}{Number\, of\, observations}$$
Enter 1 if it is true else enter 0.
The correct answer is 1
Calculate the mean of the scores of 20 students in a mathematics test:
| Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Number of students | 2 | 4 | 7 | 6 | 1 |
Find the mean of the first ten even natural numbers.
Find the mean of $$8,6,10,12,1,3,4,4$$
Find the mean of the first six prime numbers.
Find the mean of the distribution:
| Class | 1-3 | 3-5 | 5-7 | 7-10 |
| Frequency | 9 | 22 | 27 | 17 |
Find the mean of the first twelve natural numbers.
If $$45$$ persons can complete a work in $$20$$ days, then the time taken by $$75$$ persons will be ____ hours.
The enrollment of a school during six consecutive years was as follows:
$$1620,2060,2540,3250,3500,3710$$
Find the mean enrollment.
$$5$$ people were asked about the time in a week they spend in doing social work in their community. They applied $$10,7,13,20$$ and $$15$$ hours respectively. Find the mean time in a week devoted by them for social work.
The marks (out of 100) obtained by a group of students in a science test are:
$$85, 76, 90, 85, 39, 48, 56, 95, 81, 75$$
Find the:
(i) highest and lowest marks obtained by the students.
(ii) mean marks obtained by the students
Find the mean of :
$$2.1,\ 4.5,\ 5.2,\ 7.1,\ 4$$ and $$9.3$$
Find the mean of :
first six even natural number.
Find the mean of the first seven odd prime numbers.
The marks (out of 100) obtained by a group of students in a Mathematics test are $$81,72,90,90,85,86,70,93$$ and $$71$$. Find the mean marks obtained by the group of students
The mean weight of $$8$$ students is $$45.5kg$$. Two more students having weights $$41.7kg$$ and $$53.3kg$$ join the group. What is the new mean weight?
Find the mean of first eight natural numbers.
Find the mean of :
first five odd natural number.
Find the mean of :
$$7,\ 5,\ 0,\ 3,\ 0,\ 6,\ 0,\ 9,\ 1$$ and $$4$$
Find the mean of:
$$12,\ 9,\ 6,\ 11$$ and $$17$$
A student scored the following marks in $$11$$ questions of a question paper:
$$7,3,4,1,5,8,2,2,5,7,6$$
Find the median marks.
Find the mean of $$35,\ 44,\ 31,\ 57,\ 38,\ 29,\ 26,\ 36,\ 41$$ and $$43$$
Height (in $$cm$$) of $$7$$ boys of a locality are $$144\ cm,\ 155\ cm,\ 168\ cm,\ 163\ cm,\ 167\ cm,\ 151\ cm$$ and $$158\ cm$$. Find their mean height.
Find the mean of :
all prime numbers between $$20$$ and $$40$$
A can do a piece of work in 4 days and B can do the same work in 5 days. Find, how much work can be done by them working together in:
2 days.
A and B working together can do a piece of work in 10 days. B alone can do the same work in 15 days. How long will A along take to do the same work?
A and B take 6 hours and 9 respectively to complete a work . A works for 1 hour and then B works for two hours.
How much work is done in the these 3 hours?
A can do a piece of work in 6 days and B can do it in 8 days. How long will they take to complete it together?
Find the mean of :
all prime numbers upto $$30$$
Shaded can prepare one wooden chair in 3 days and shaif prepare the same chair in 4 days. If they work together, in how many days will they prepare?
one chair?
14 chairs of the same kind?
A can do a piece of work in 4 days and B can do the same work in 5 days. Find, how much work can be done by them working together in:
One day
Joseph and peter can complete a work in 20 hours and 25 hours respectively. Find:
work done left after both worked together for 4 hrs.
A, B and C can do a piece of work in 12 , 15 and 20 days respectively. How long will they take to do it working together?
two taps can fill a cistern in 10 hours and 8 hours respectively. A third tap can empty it in 15 hours. How long will it take to fill the empty cistern, if all of them are opened together?
Mohit can complete a work in 50 days, whereas Anuj can complete the same work in 40 days. Find:
work left after Mohit has worked on it for 20 days.
Joseph and peter can complete a work in 20 hours and 25 hours respectively. Find:
Time taken by peter to complete the remaining work.
Joseph and peter can complete a work in 20 hours and 25 hours respectively. Find:
work done by both together in 4 hrs.
A is able to complete 1/3 of a certain work in 10 hrs and B is able to complete 2/5 of the same work in 12 hrs.Find :
how much work can A do in 1 hours?
Mohit can complete a work in 50 days, whereas Anuj can complete the same work in 40 days. Find:
work done by mohit in 20 days.
A and B take 6 hours and 9 respectively to complete a work . A works for 1 hour and then B works for two hours.
How much work is still left?
Mohit can complete a work in 50 days, whereas Anuj can complete the same work in 40 days. Find:
time taken by Anuj to complete the remaining work.
A is able to complete 1/3 of a certain work in 10 hrs and B is able to complete 2/5 of the same work in 12 hrs.Find
Work done by B in 1 hour
The average of n numbers $$x_1, x_2, x_3 ..... x_n$$ is A.
If $$x_1$$ is replaced by $$(x + a) x_1, x_2$$ is replaced by $$(x + a) x_2$$ and so on. Find the new average.
A, B and C together finished a work in a 4 days. If a alone can finish the same work in 8 days and B in 12 days, find how long will C take to finished the work .
The mean of $$5$$ observations is $$50$$. One of the observations was removed from the data, hence the mean became $$45$$. Find the observation which was removed.
The mean of $$x, x+2, x+4, x+6$$ and $$x + 8$$ is 11, find the mean of the first three observations.
Shaheed can prepare one wooden chair in 3 days and Shaif can prepare the same chair in 4 days. If they work together, in how many days will they prepare:
one chair?
14 chairs of the same kind?
The heights (in cm) of the volley-ball players from team A and team B were recorded as:
Team A: 180, 178, 176, 181, 190, 175, 187
Team B: 174, 175, 190, 179, 178, 185, 177
Which team had the greater average height?
A is able to complete 1/3 of a certain work in 10 hrs and B is able to complete 2/5 of the same work in 12 hrs.Find
in how much time will the work be complete, if work together?
A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
| No. of plants | 0 - 2 | 2 - 4 | 4 - 6 | 6 - 8 | 8 - 10 | 10 - 12 | 12 - 14 |
| No. of Houses | 1 | 2 | 1 | 5 | 6 | 2 | 3 |
There are $$40$$ students in a class, out of them $$15$$ are boys. The mean of marks obtained by boys is $$33$$ and that for girls is $$35$$. Find out the mean of all students in the class.
The table below shows the daily expenditure on food of 25 households in a locality.
Find the mean daily expenditure on food by a suitable method.
| Daily Expenditure (Rs.) | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 |
| No. of Households | 4 | 5 | 12 | 2 | 2 |
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
| Literacy rate (in %) | 45 - 55 | 55 -65 | 65 - 75 | 75 - 85 | 85 - 95 |
| Number of Cities | 3 | 10 | 11 | 8 | 3 |
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
(i) $$ n=30, \therefore \dfrac{n}{2}=15 $$
Class interval having median is $$ (55-60) $$
$$ \begin{aligned} 1=55, n=30, f &=6, c f=13, h=5 \\ \therefore \text { Median } &=l+\left[\dfrac{\dfrac{n}{2}-c f}{f}\right] \times h \\ &=55+\left(\dfrac{15-13}{6}\right) \times 5 \\ &=55+\dfrac{2}{6} \times 5 \end{aligned} $$
$$ =55+1.67 $$
$$ \therefore $$ Median $$ =56.67 \mathrm{kg} . $$
Class interval having median is $$ (55-60) $$
$$ \begin{aligned} 1=55, n=30, f &=6, c f=13, h=5 \\ \therefore \text { Median } &=l+\left[\dfrac{\dfrac{n}{2}-c f}{f}\right] \times h \\ &=55+\left(\dfrac{15-13}{6}\right) \times 5 \\ &=55+\dfrac{2}{6} \times 5 \end{aligned} $$
$$ =55+1.67 $$
$$ \therefore $$ Median $$ =56.67 \mathrm{kg} . $$
Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarized as follows. Find the mean heartbeats per minute for these women, choosing a suitable method
| No. of heart- beats per minutes | 65 - 68 | 68 - 71 | 71 - 74 | 74 - 77 | 77 - 80 | 80 - 83 | 83 - 86 |
| No. of women | 2 | 4 | 3 | 8 | 7 | 4 | 2 |
To find out the concentration of $$ SO_{2} $$ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
| Concentration $$ SO_{2} $$ (in ppm) | Frequency |
| 0.00 - 0.04 | 4 |
| 0.04 - 0.08 | 9 |
| 0.08 - 0.12 | 9 |
| 0.12 - 0.16 | 2 |
| 0.16 - 0.20 | 4 |
| 0.20 - 0.24 | 2 |
A class teacher has the following absentee record of 40 students of a class for the whole term.
Find the mean number of days a student was absent.
| No. of Days | 0 - 6 | 6 - 10 | 10 - 14 | 14 - 20 | 20 - 28 | 28 - 39 | 39 - 40 |
| No. of students | 11 | 10 | 7 | 4 | 4 | 3 | 1 |
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
| Literacy rate (in %) | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 | 85 - 95 |
| Number of cities | 3 | 10 | 111 | 8 | 3 |
Assumed mean = a = 70
Class size = h = 10
$$ \mathbf{Mean} = \bar{x} = a + \dfrac{\sum f_{i}u_{i}}{\sum f_{i}} \times h $$
$$ = 70 + \dfrac{-2}{35} \times 10 $$
$$ = 70 - \dfrac{20}{35} = 70 - 0.57 $$
$$ = 69.43 $$%
$$ \therefore $$ Mean literacy rate is 69.43%
Class size = h = 10
$$ \mathbf{Mean} = \bar{x} = a + \dfrac{\sum f_{i}u_{i}}{\sum f_{i}} \times h $$
$$ = 70 + \dfrac{-2}{35} \times 10 $$
$$ = 70 - \dfrac{20}{35} = 70 - 0.57 $$
$$ = 69.43 $$%
$$ \therefore $$ Mean literacy rate is 69.43%
Calculate the mean for the following frequency distribution
| Mark | 15 - 19 | 20 - 24 | 25 - 29 | 30 - 34 | 35- 39 | 40- 44 |
| Frequency | 6 | 5 | 9 | 12 | 6 | 2 |
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.Find the missing frequency f.
| Daily pocket allowance (Rs.) | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 | 19 - 21 | 21 - 23 | 23 - 25 |
| No. of Children | 7 | 6 | 9 | 13 | f | 5 | 4 |
Find the mean of the first 7 natural numbers.
The following are the marks scored in a unit test ( out of 25 ) . Prepare a frequency distribution table , taking class interval as 0 - 4 , 5 - 9 , 10 - 14 , 15 - 19 , 20 - 24.
21 , 14 , 3 , 7 , 23 , 18 , 24 , 16 , 18 , 17 , 18 , 21 , 23 , 19 , 12 , 14 , 11 . From the table
Find the midpoint of each class interval .
Mid points of $$0-4 , 5 - 9 , 10 - 14 , 15 - 19 ,$$ and $$20 - 24$$ are $$2 , 7 , 12 , 17$$ and $$22$$ respectively .
If the mean of 8 , 12 , 21 , 42 x is 20 find the value of x.
The mark obtained by 12 student in a mathematics examination are given below 48, 78 , 93 , 90 , 66 , 54 , 83 , 58 , 60 , 75 , 89 , 84 .
the mean mark of the student if each student is given 4 grace marks .
The mark obtained by 12 student in a mathematics examination are given below 48, 78 , 93 , 90 , 66 , 54 , 83 , 58 , 60 , 75 , 89 , 84 .
Find the mean of the marks
Find the mean for the following distribution 12 , 14 , 10, 12,18 ,10 , 15 , 11 , 19 , 20 , 12 , 15 , 19 , 10 , 18 , 16 , 20 , 17.
Find mean variable for frequency distribution
| Class | 0-30 | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 |
| Frequency | 2 | 3 | 5 | 10 | 3 | 5 | 2 |
Fins mean and stander deviation by shortcut method .
| $$x_{i}$$ | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 |
| $$f_{i}$$ | 2 | 1 | 12 | 29 | 25 | 12 | 10 | 4 | 5 |
Find mean and variance for the data
| $$x_{i}$$ | 82 | 83 | 87 | 88 | 92 | 94 | 99 |
| $$f_{i}$$ | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
Find mean variable for frequency distribution
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| frequency | 5 | 8 | 15 | 16 | 6 |
Calculate arithmetic mean of marks obtained in English in monthly test of 10 students.
| S. No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mark obtained | 30 | 28 | 32 | 12 | 18 | 20 | 25 | 15 | 26 | 14 |
The monthly salary (in Rs.) of assistant workers in a school are Rs.1720, Rs.1750, Rs.1760 and Rs1710, then find arithmetic mean.
The average weight of 25 students of group A of a class is 51 kg. Whereas average weight of 35 students of group B is 54 kg. Find the average weight of 60 students of this class
The number of books issued to students in 10 days from library of a school are as follows:
| 300 | 405 | 455 | 489 | 375 | 280 | 418 | 502 | 300 | 476 |
If marks obtained by 10 students in maths are 52, 75, 40, 70, 43, 40, 65, 35, 48 and 52 then find arithmetic mean.
If arithmetic mean of digits 3, 4, 8, 5, x, 3, 2, 1 is 4, then find x.
Two candidates A and B scored following marks in different subject for entrance examination in Business School whose weightage are given along with: (Refer table)
By finding weightage mean find from A and B which is more capable?
Find mean , variable and standard by short - cut method
| Height (cm) | 70 - 75 | 75-80 | 80-85 | 85-90 | 90-95 | 95-100 | 100-105 | 105-110 | 110-115 |
| No. of student | 3 | 4 | 7 | 7 | 15 | 9 | 6 | 6 | 3 |
Runs scored in 10 innings by a cricketer are 60, 62, 56, 64, 0, 57, 33, 27, 9 andFind average run scored in these innings.
There are $$45$$ students in a class in which $$15$$ are girls. Average weight of girls is $$45$$ kg and of boys $$52$$ kg. Find average weight of one student.
Find the (arithmetic) of following frequency distribution
| $$ x $$ | 0.1 | 0.3 | 0.5 | 0.7 | 0.89 |
| $$ f $$ | 7 | 8 | 10 | 15 | 10 |
Table for A.M.
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{27.5}{50} = 0.55 $$
Thus, required A.M. =0.55
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{27.5}{50} = 0.55 $$
Thus, required A.M. =0.55
The number of children in 100 families is as follows :
| No. of children | 1 | 2 | 3 | 4 | 5 | 6 |
| No. of families | 45 | 25 | 19 | 8 | 2 | 1 |
Calculation for arithmetic mean
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum fx}{\sum f} = \frac{200}{100} = 2 $$
Thus, arithmetic mean = 2
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum fx}{\sum f} = \frac{200}{100} = 2 $$
Thus, arithmetic mean = 2
Marks obtained by a student in Mathematics in three monthly tests are 85, 60 and 75 resp. And in annual exams he got 95 marks. Weightage of monthly tests are same where as weightage of annual exams is double that of monthly exams. Find the mean weightage of marks in Mathematics.
Weight of students in a class are given in following table :
| Weight (in kg.) | No. of students |
| 20 | 1 |
| 21 | 2 |
| 22 | 6 |
| 23 | 7 |
| 24 | 4 |
| 25 | 2 |
| 26 | 3 |
| 27 | 2 |
| 28 | 3 |
Table for A.M.
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{717}{30} = 23.9 $$
Thus, required A.M. = 23.9
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{717}{30} = 23.9 $$
Thus, required A.M. = 23.9
Find the mean (arithmetic) of following frequency distribution
| $$ x $$ | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 |
| $$ f $$ | 30 | 60 | 20 | 40 | 10 | 50 |
Table for A.M.
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{72}{210} = 0.34 $$
Thus, required A.M. = 0.34
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{72}{210} = 0.34 $$
Thus, required A.M. = 0.34
Find the mean (arithmetic) of following frequency distribution
| $$ x $$ | 3 | 5 | 8 | 11 |
| $$ f $$ | 2 | 4 | 5 | 3 |
Find the mean (arithmetic of following frequency distribution
| $$ x $$ | 2 | 5 | 7 | 9 | 11 |
| $$ f $$ | 1 | 5 | 4 | 7 | 3 |
Table of A.M.
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{151}{20} = 7.55 $$
Thus, required A.M. = 7.55
Thus, arithmetic mean $$ (\bar{x}) = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{151}{20} = 7.55 $$
Thus, required A.M. = 7.55
Find the mean (arithmetic) of following frequency distribution :
| Weight (in kg) | 60 | 61 | 62 | 63 | 64 | 65 |
| No. of workers | 5 | 8 | 14 | 16 | 10 | 7 |
The salary of employees in a factory are according to following table :
| Monthly salary (in Rs.) | 1000 - 1200 | 1200 - 1400 | 1400 - 1600 | 1600 - 1800 | 1800 - 2000 |
| No. of employees | 10 | 20 | 20 | 15 | 5 |
Calculation of arithmetic mean :
Arithmetic mean = $$ \frac{\sum f_{i}x{i}}{\sum f_{i}} =\dfrac {102000}{70} = 1457.14 $$
Thus, arithmetic mean of salary = Rs. 1457.14
Arithmetic mean = $$ \frac{\sum f_{i}x{i}}{\sum f_{i}} =\dfrac {102000}{70} = 1457.14 $$
Thus, arithmetic mean of salary = Rs. 1457.14
Find the mean (arithmetic) of following frequency distribution
| Marks $$ (x) $$ | 100 - 120 | 120 - 140 | 140 - 160 | 160 - 180 | 180 - 200 |
| No. of Students | 10 | 20 | 20 | 15 | 5 |
Calculation of arithmetic mean :
Arithmetic mean $$ = \frac{\sum f_{i}x_{i}}{\sum f_(i)} = \frac{10200}{70} = 145.71 $$
Thus, required arithmetic mean = 145.71
Arithmetic mean $$ = \frac{\sum f_{i}x_{i}}{\sum f_(i)} = \frac{10200}{70} = 145.71 $$
Thus, required arithmetic mean = 145.71
Find the mean (arithmetic) of following frequency distribution
| Class | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 |
| Frequency | 6 | 10 | 8 | 12 | 4 |
Calculation of arithmetic mean :
Arithmetic mean = $$ \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{1980}{40} = 49.5 $$
Thus, required arithmetic mean = 49.5
Arithmetic mean = $$ \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{1980}{40} = 49.5 $$
Thus, required arithmetic mean = 49.5
Find the mean (arithmetic) of following frequency distribution
| Class | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| Frequency | 9 | 12 | 15 | 10 | 14 |
Calculation of arithmetic mean
Arithmetic mean $$ = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{1580}{60} = 26.33 (approx) $$
Arithmetic mean $$ = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{1580}{60} = 26.33 (approx) $$
Find the mean (arithmetic) of following frequency distribution :
| $$ x $$ | 800 | 820 | 860 | 900 | 920 | 980 | 1000 |
| $$ f $$ | 7 | 14 | 19 | 25 | 20 | 10 | 5 |
Let A = 900, h = 20
Table of find arithmetic mean :
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum u_{i}f_{i}}{\sum f_{i}} \times h = 900 + \frac{-44}{100} \times 20 = 900 - 8.8 = 891.2 $$
Thus, required arithmetic mean =891.2
Table of find arithmetic mean :
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum u_{i}f_{i}}{\sum f_{i}} \times h = 900 + \frac{-44}{100} \times 20 = 900 - 8.8 = 891.2 $$
Thus, required arithmetic mean =891.2
| x | 5 | 6 | 7 | 8 | 9 |
| f | 4 | 8 | 14 | 11 | 3 |
Arithmetic mean $$(\bar{x}) = \frac{\sum f_i x_i}{\sum f_i} = \frac{281}{40} = 7.025$$
Thus, arithmetic mean = 7.025
Thus, arithmetic mean = 7.025
Find arithmetic mean from the frequency distribution.
Let A = 50, h = 4
Arithmetic mean $$(\bar{x}) = \frac{\sum u_if_i }{\sum f_i} \times h $$
$$= 50 + \frac{5}{30} \times 4 = 50 + \frac{2}{3} = 50 - 0.67 = 50.67$$
Thus, required A.M. = 50.67
Arithmetic mean $$(\bar{x}) = \frac{\sum u_if_i }{\sum f_i} \times h $$
$$= 50 + \frac{5}{30} \times 4 = 50 + \frac{2}{3} = 50 - 0.67 = 50.67$$
Thus, required A.M. = 50.67
Find mean of the following frequency distribution :
| Wt. (in kg) | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| No. of Students | 10 | 25 | 28 | 12 | 10 | 15 |
Arithmetic mean $$ = \frac{\sum f_{i}x_{i}}{\sum f_{i}} = \frac{6820}{100} = 68.2 $$
Thus, frequency distribution mean = 68.2
Thus, frequency distribution mean = 68.2
Find the mean (arithmetic) of following frequency distribution
| Class | 0 - 6 | 6 - 12 | 12 - 18 | 18 - 24 | 24 - 30 |
| Frequency | 6 | 8 | 10 | 9 | 7 |
Calculation of arithmetic mean
Arithmetic mean $$ = \frac{ \sum f_{i}x_{i}}{ \sum f_{i}} = \frac{618}{40} = 15.45 $$
Arithmetic mean $$ = \frac{ \sum f_{i}x_{i}}{ \sum f_{i}} = \frac{618}{40} = 15.45 $$
Find the mean (arithmetic) of following frequency distribution :
| Expenditure (in Rs.) | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 | 350 - 400 | 400 - 450 | 450 - 500 |
| No. of workers | 24 | 40 | 33 | 28 | 30 | 22 | 16 | 7 |
Let A = 275, h = 50
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum u_{i}f_{i}}{\sum f_{i}} \times h = 275 - \frac{35}{200} \times 50 = 275 - 8.75 = 266.25 $$
Thus, required arithmetic mean = 266.25
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum u_{i}f_{i}}{\sum f_{i}} \times h = 275 - \frac{35}{200} \times 50 = 275 - 8.75 = 266.25 $$
Thus, required arithmetic mean = 266.25
Find mean from the following frequency distribution :
| Class-interval | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| Frequency | 10 | 25 | 28 | 12 | 10 | 15 |
Let A = 65, h = 10
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum u_{i}f_{i}}{\sum f_{i}} \times h = 65 + \frac{32}{100} \times 10 $$
$$ = 65 + 3.2 = 68.2 $$
Thus, required A.M. = 68.2
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum u_{i}f_{i}}{\sum f_{i}} \times h = 65 + \frac{32}{100} \times 10 $$
$$ = 65 + 3.2 = 68.2 $$
Thus, required A.M. = 68.2
Find mean of the following frequency distribution taking assumed mean 25.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| $$ f $$ | 6 | 10 | 13 | 7 | 4 |
Let assumed mean (A) = 25
Table for calculation of arithmetic mean :
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum f_{i}d_{i}}{\sum f_{i}} = 25 + \frac{-70}{40} = 25 - 1.75 = 23.25 $$
Thus, required arithmetic mean = 23.25
Table for calculation of arithmetic mean :
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum f_{i}d_{i}}{\sum f_{i}} = 25 + \frac{-70}{40} = 25 - 1.75 = 23.25 $$
Thus, required arithmetic mean = 23.25
If the mean of $$3,7,11$$ and $$x$$ is $$9$$, what is the value of $$x$$?
in the following table, age distribution of patients suffering from a disease in a specify class in a city are given. Find average age (in yrs) per patient.
| Age (in yrs) | 5-14 | 15-24 | 25-34 | 35-44 | 45-54 | 55-64 |
| No. of patients | 6 | 11 | 21 | 23 | 14 | 5 |
Let assumed mean (A) = 29.5
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum f_{i}d_{i}}{\sum f_{i}} = 29.5 + \frac{430}{80} = 29.5 + 5.37 = 34.87 $$
Thus, arithmetic mean = 34.87 yrs
Arithmetic mean $$ (\bar{x}) = A + \frac{\sum f_{i}d_{i}}{\sum f_{i}} = 29.5 + \frac{430}{80} = 29.5 + 5.37 = 34.87 $$
Thus, arithmetic mean = 34.87 yrs
Find the mean )arithmetic) of following frequency distribution :
| Expenditure on water (in Rs.) | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 |
| No. of Houses | 7 | 5 | 7 | 8 | 9 | 11 | 7 | 5 | 4 | 4 | 3 |
Let A = 42.5, h = 5
Arithmetic mean $$ = A + \frac{\sum f_{i}u_{i}}{\sum f_{i}} \times h = 42.5 + \frac{-41}{70} \times 5 = 42.5 - 2.93 = 39.57 $$
Thus, required A.M. = 39.57
Arithmetic mean $$ = A + \frac{\sum f_{i}u_{i}}{\sum f_{i}} \times h = 42.5 + \frac{-41}{70} \times 5 = 42.5 - 2.93 = 39.57 $$
Thus, required A.M. = 39.57
The average income of 20 employees is RsLater it was discovered that income of 2 employees was recorded as 120 and 80 instead of 40 andFind the correct mean.
The Patel family flies from their home town, H, to Kiruna , K , in Lapland.
The Patel family has six suitcases.
The number of items in each suitcase is shown below.
$$15 $$ $$16$$ $$16$$ $$18$$ $$19$$ $$21$$
Calculate the mean.
In a class of 50 students, 10 have failed and their average of marks is 2.The total secured by the entire class wereFind the average marks those who have passed.
Write the merits and demerits of the arithmetic mean.
$$8$$ men and $$10$$ boys do a work in the same days as $$ 4 $$ men and $$16$$ boys do. $$ 1$$ man and $$3$$ boys start a work to finish it in $$40$$ days. After eighteen days, $$\dfrac{9}{20}$$ th part of work had been finished. How many boys should be increased to make the work complete in exact time ?
X complete a piece of work in $$20$$ days and Y complete it in $$30$$ days and Z complete it in $$ 60$$ days. At first day to every third day Y and every fourth day Z helped X. At how many days will complete the work?
$$20$$ men can complete the work in $$40$$ days. When should $$4$$ men leave so that the work may be finished in $$48$$ days?
One pump working continuously can fill a reservoir in thirty days. A second pump can fill the reservoir in twenty days. How long would it take both pumps working together to fill the reservoir?
The number of children in $$10$$ families in a locality are $$2, 4, 3, 4, 1, 6, 4, 5, x, 5$$. Find $$x$$ if the mean number of children in a family is $$4$$.
Tap $$A$$ can fill a cistern in $$8$$ hours and tap $$B$$ can empty it in $$12$$ hours. How long will it take to fill cistern if both of them are opened together?
From a tin sheet, a sector of radius 20 centimetres and central angle $$240^o$$ is divided into four equal parts as shown in the figure. Then the shaded portion is cut off. Using this, a vessel in the shape of a square pyramid is made.
What is the capacity of this vessel?
The number of hours needed to assemble computers varies directly as the number of computers and inversely as the number of workers. If $$4$$ workers can assemble $$12$$ computers in $$9$$ hours, how many workers are needed to assemble $$48$$ computers in $$8$$ hours?
Find the volume of a regular tetragonal pyramid if a side of its base is "a" long and the base dihedral angle is $$\alpha$$.
Side of the base $$=a$$
Base dihedral angle $$=\alpha$$
Attitude $$=?$$
$$\Rightarrow \tan\;\alpha=\dfrac{x}{a}$$
$$\Rightarrow x=a\tan\alpha$$
$$\Rightarrow$$ Attitude $$ =a\tan\alpha$$
$$\Rightarrow$$ Volume $$=\dfrac{2}{3}\left( a^2-x^2\right)x$$
$$=\dfrac{2}{3}\left( a^2-a^2\tan^2\alpha\right)a\tan \alpha$$
$$=\dfrac{2}{3}a^3\left(1-\tan^2\alpha\right)\tan \alpha.$$
Hence, the answer is $$\dfrac{2}{3}a^3\left(1-\tan^2\alpha\right)\tan \alpha.$$
A and B together can do a piece of work in $$20$$ days, B and C together can do it in $$15$$ days while C and A together can do it in $$12$$ days. how long will they take to finish the work, working all together? how long would each take to do the same work?
If $$20\ $$men can build a wall $$ 56m\ $$long in $$6 $$days, what length of a similar wall can be built by $$ 35$$ men in$$ 3$$ days?
In a regular tetragonal pyramid the altitude is 3 cm long and a lateral edge is 5 cm long. Find the volume of the pyramid.
A can do a piece of work in 24 days while B can do it in 30 days. In how many days can they complete it, if they work together ?
Find the speed in each case :
A train covers $$300\ km$$ in $$4$$ hours.
$$120$$ men had provision for food $$ 195$$ days.After $$5$$ days, $$30$$ men died died due to a disease. How long will the remaining food last?
$$A ,B$$ and $$C$$ working together can finish a piece of work in $$8$$ hours . A alone can do it in $$20$$ hours and $$B$$ alone can do it in $$24$$ hours In how many hours will $$C$$ alone do the same work?
$$12$$ men working $$8 $$hrs a day complete a piece of work in $$10$$ days. To complete the same work in$$ 8\ $$days, working $$ 15$$ hrs a day, how many men are needed?
Compute the mean of the following data:
Sunil takes $$5$$ days more than Anil to complete a certain work. $$4$$ day after starting the work, Anil left the work. The remaining work was done by Sunil in $$5$$ days. Find how many days each will take to complete the work.
Two men can do a piece of work in $$6$$hours and $$4$$ hours respectively. After the first has worked for $$2$$ hours, he is joined by the other. By when should the work be completed.
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Find the mean of the following distribution .
What will be the value of the resulting mean if each observation is
(ii) Divided by 2?
| $${ x }_{ 1 }$$ | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
| $${ f }_{ 1 }$$ | 4 | 5 | 8 | 17 | 6 | 8 | 4 |
At Deoprayag (Garhwal, UP) river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Suppose Alaknanda has a width of $$12\ m$$, Bhagirathi has a width of $$8\ m$$ and Ganga has a width of $$16\ m$$. Assume that the depth of water is same in the three rivers. Let the average speed of water in Alaknanda be $$20\ km\ h^{-1}$$ and in Bhagirathi be $$16\ km\ h^{-1}$$ Find the average speed of water in the river Ganga.
A boat goes $$30$$ km upstream and $$44$$ km downstream in $$10$$ hours. In $$13$$ hours it can go $$40$$ km upstream and $$55$$ km downstream. Determine the speed of the stream and that of the boat in still water.
$$A$$ and $$B$$ can finish a piece of work in $$16$$ days and $$12$$ days respectively. A started the work and worked at it for $$2$$ days. He was then joined by B. Find the total time taken to finish the work.
A certain student found it necessary to decipher an ols manuscript. During previous experience of the same kind he had observed that the number of words he could read daily varied jointly as the number of moles he walked and the number of hours be worked during the day. he therefore gradually increased the amount of daily exercise and daily work at the rate of $$1$$ mile and $$1$$ hour per day respectively, neginning the first day with his usual quantity. He found that the manuscript contained $$232000$$ words that he counted $$12000$$ on the first day adn $$72000$$ on the last day; and that by the end of half the time he had counted $$62000$$ words: find his usual amount of daily exercise and work.
Raman alone can finish a piece of work in $$15$$ days and Suman alone can do it in $$18$$ days if both of them work it together. How much time will they take to finish it?
Find the volume of the greatest sphere that can be cut of a cube of side $$14\ cm$$. Find also the volume of the remaining piece.
The greatest sphere will be such that diameter of sphere = side of cube
$$ \therefore $$ radius of sphere $$ = 14\ cm \div 2 = 7\ cm $$
Volume of sphere $$ = \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \times \dfrac{22}{7} \times 7 \times 7 \times 7\ cm^{3} = 1437.3\ cm^{3} $$
Volume of cube $$ = (14 \times 14 \times 14)\ cm^{3} = 2744\ cm^{3} $$
$$ \therefore $$ Volume of remaining piece $$ = (2744 - 1437.3)\ cm^{3} = 1306.7\ cm^{3} $$
$$ \therefore $$ radius of sphere $$ = 14\ cm \div 2 = 7\ cm $$
Volume of sphere $$ = \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \times \dfrac{22}{7} \times 7 \times 7 \times 7\ cm^{3} = 1437.3\ cm^{3} $$
Volume of cube $$ = (14 \times 14 \times 14)\ cm^{3} = 2744\ cm^{3} $$
$$ \therefore $$ Volume of remaining piece $$ = (2744 - 1437.3)\ cm^{3} = 1306.7\ cm^{3} $$
Two taps $$A$$ and $$B$$ together fill a swimming pool in $$15$$ days.Taps $$A$$ and B are kept open for $$12$$ days and then tap $$B$$ is closed. It takes another $$8$$ day for the swimming pool to be filled. How many days does each tap require to fill the swimming pool?
Class 11 Commerce Applied Mathematics Extra Questions
- Basics Of Financial Mathematics Extra Questions
- Circles Extra Questions
- Descriptive Statistics Extra Questions
- Differentiation Extra Questions
- Functions Extra Questions
- Limits And Continuity Extra Questions
- Logarithm And Antilogarithm Extra Questions
- Mathematical And Logical Reasoning Extra Questions
- Number Theory Extra Questions
- Numerical Applications Extra Questions
- Permutations And Combinations Extra Questions
- Probability Extra Questions
- Relations Extra Questions
- Sequences And Series Extra Questions
- Set Theory Extra Questions
- Straight Lines Extra Questions
- Tangents And Its Equations Extra Questions