Direct And Inverse Proportions - Class 8 Maths - Extra Questions

How many men must be engaged to do a piece of work in 16 days which 24 men can do in 40 days ?



If 30 men can reap a field in 14 days, in how many days will 20 men reap it ?



Fill in the blanks in each of the following so as to make the statement true:
Two quantities are said to vary ... with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same. 



$$252$$ students take $$3$$ hours for decorating the school. If $$372$$ students together do this work, then this work completes in how much time(in hours)?



Which of the following are in inverse proportion?

(i) The number of workers on a job and the time to complete the job.

(ii) The time taken for a journey and the distance travelled in a uniform speed.

(iii) Area of cultivated land and the crop harvested.

(iv) The time taken for a fixed journey and the speed of the vehicle.

(v) The population of a country and the area of land per person.



Complete the following table if $$x \propto y$$.
$$x$$$$1$$$$2$$$$3$$$$-$$$$5$$
$$y$$$$4$$$$8$$$$-$$$$16$$$$-$$



Ektaben could buy eleven similar purses in $$Rs. 1320$$, if she gives $$Rs. 960$$, then how many such purse could she buy?



The cube root of $$x$$ varies inversely as the square of $$y$$. If $$x=8$$ when $$y=3$$, then find $$x$$ when $$y=1\displaystyle\frac{1}{2}$$.



Total $$100\ kg$$ wheat is to be filled in $$5$$ jute bags of equal size, then in such $$7$$ jute bags how much kilogram wheat is to be filled?



Four boxes of equal sizes contain $$240\ soaps$$, then in such three boxes how many soaps are there?



$$3600$$ litre water is needed to fill up six tanks of equal sizes, then with $$8400$$ litre water how many such tanks are needed?



To buy $$8$$ waterbags of equal size $$Rs. 560$$ is necessary, then how much amount is necessary to buy five such waterbags in rupees?



If $$x$$ and $$y$$ are directly proportional, find the value of $$x_1,x_2$$ and $$y_1$$ in the table given below:
$$x$$$$3$$$$x_1$$$$x_2$$$$10$$
$$y$$$$72$$$$120$$$$192$$$$y_1$$



If $$20$$ litre oil is fill up into $$4$$ jars, then what is the capacity of $$7$$ such jars?



If $$a,b,c,d$$ are in continued proportion, prove that
$$(a+d)b+c)-(a+c)(b+d)={(b-c)}^{2}$$ 



At a party, $$8$$ bottles of soft drink are served for every  batch of $$5$$ children. How many bottles would be served if $$40$$ children were present at the party ?



Observe the table given below and in the case find whether $$x$$ and $$y$$ are inversely proportional:
$$x$$$$6$$$$10$$$$14$$$$16$$
$$y$$$$9$$$$15$$$$21$$$$24$$



If $$x$$ and $$y$$ are inversely proportional, find the values of $$X_1, X_2$$ and $$Y_1, Y_2$$ in the table given below:
$$x$$$$8$$$$X_1$$$$16$$$$X_2$$$$80$$
$$y$$$$Y_1$$$$4$$$$5$$$$2$$$$Y_2$$



Observe the table given below and in the case find whether $$x$$ and $$y$$ are inversely proportional:
$$x$$$$9$$$$3$$$$6$$$$36$$
$$y$$$$4$$$$12$$$$9$$$$1$$



A fist with a mass of $$3\ kg$$ causes a fishing pole to bend $$9\ cm$$. If the amount of bending varies directly as the mass, how much will the pole bend for a $$2\ kg$$ fish ? 



$$m:n$$



Which of the following are in inverse proportion ? 
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed. 
(iii) Area of cultivated land and the crop harvested. 
(iv) The time taken for a fixed journey and the speed of the vehicle. 
(v) The population of a country and the area of land per person.



If 18 men can do a piece of work in 18 days, how many men would do it in 27 days ?



In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

Number of winners
1
2
4
5
8
10
20
Prize for each winner (in Rs.)
1,00,000
50,000
...
...
...
...
...



A $$5\ m$$ $$60\ cm$$ high vertical pole casts a shadow $$3\ m$$ $$20\ cm$$ long. Find at the same time (i) the length of the shadow cast by another pole $$10\ m$$ $$50\ cm$$ high (ii) the height of a pole which casts a shadow $$5\ m$$ long.



Kanchanben distributes some chocolates among $$300$$ students, then one would get $$4$$ chocolates. If she distributes same chocolates among $$400$$ students then one would get how much chocolates?



Following are the car parking charges near a railway station up to 
 Time Parking charges
 4 hours Rs. 60
 8 hours Rs. 100
 12 hours Rs. 140
 24 hours Rs. 180
Check if the parking charges are in direct proportion to the parking time.



Suppose $$2$$ kg of sugar contains $$9 106$$ crystals. How many sugar crystals are there in (i) $$5$$ kg of sugar? (ii) $$1.2$$ kg of sugar?



Rashmi has a road map with a scale of $$1$$ cm representing $$18$$ km. She drives on a road for $$72$$ km. What would be her distance covered in the map?



The cost of $$\cfrac{19}{4}$$ meter of wire is Rs. $$\cfrac{171}{2}$$. Find the cost of one meter of the wire.



A man had to walk a certain distance. He covered two thirds of it at $$4$$ kmph and the remaining at $$5$$ kmph. If the total time taken is $$42$$ minutes, find the total distance.
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In a Television game show, the prize money of Rs $$1,00,000$$ is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?

Number of winners   $$1$$    $$2$$    $$4$$    $$5$$  $$8$$ $$10$$ $$20$$
Prize of each winner (in Rs)$$1,00,000$$ $$50,000$$ $$\cdots$$$$\cdots$$$$\cdots$$$$\cdots$$$$\cdots$$ 



Two persons could fit new windows in a house in $$3$$ days.

(i) One of the persons fell ill before the work started. How long would the job take now?

(ii) How many persons would be needed to fit the windows in one day?



A farmer has enough food to feed $$20$$ animals in his cattle for $$6$$ days. How long would the food last if there were $$10 $$ more animals in his cattle?



A printing machine takes $$15$$ minute to print three pages of a book. If the book contains $$56$$ pages, then how much time(in minutes) is taken to print total book by this machine?



In a class $$15$$ benches are there. $$4$$ students are sitting on each bench. If number of students remains same and $$12$$ benches are there then on each bench how many students have to sit?



In a school, on a clean village-day $$150$$ students takes $$6$$ hours to clean village, if $$180$$ students do this work, then find time taken to clean the village completely in hours is



In a school, during cultural activity programme, donation obtained from donor is distributed among $$33$$ winning students then each would get $$Rs. 80$$. If this amount is distributed among winners of sports-competition, then each would get $$Rs. 120$$, then how many students win the sports-competition?



Out of $$450$$ flowers $$9$$ garlands are prepared of equal size, then how many garlands are prepared from such $$600$$ flowers?



Amount of blind person fund collected from a school of a village is distributed among $$81$$ persons, then each would get $$Rs. 600$$. If the same amount is distributed among $$54$$ persons then find the amount obtained by each person in rupees.



Mansukhbhai distributes some kg of grains among $$150$$ persons then each would get $$7\ kg$$ grains, whereas Jitubhai distributes same kg of grains among $$210$$ persons, then how much amount(in kg) of grains each would get?



If $$y$$ varies inversely with the fourth root of x, and $$y = 4$$ when $$x =\frac{1}{16}$$, then what is the value of $$y$$ when $$x = \dfrac{1}{81}$$ ?



Observe the following tables and find if $$x$$ and $$y$$ are directly proportional:
$$x$$$$5$$$$8$$$$12$$$$15$$$$18$$$$20$$
$$y$$$$15$$$$24$$$$36$$$$60$$$$72$$$$100$$



If 36 men can do a piece of work in  25 days, in how many days will 15 men do it ?



In a culture, the bacteria count is $$1,00,000$$. The number is increased by $$10\%$$ in $$2$$ hours. In how many hours will the count reach $$2,00,000$$, if the rate of growth of bacteria is proportional to the number present?



If $$y$$ varies inversely as $$x$$, and $$y = 9$$ when $$x = 2$$, find $$y$$ when $$x = 3$$. 



A train takes $$2$$ hours to travel from Ajmer to Jaipur, which are $$130\ km$$ apart. How much time will it take to travel from Delhi to Bhopal which are $$780\ km$$ apart if the train is travelling at the uniform speed.



Following are the car parking charges near railway station upto 
$$4$$ hrs          $$Rs\;60$$
$$8$$ hrs          $$Rs\;100$$
$$12$$ hrs        $$Rs\;140$$
$$24$$ hrs        $$Rs\;180$$
Check if the parking charges are in direct proportion to the parking time.



A work force 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 ?



Twenty pillows can be bought for $$Rs\ 5120$$ How many pillows can be bought for $$Rs\ 7936 $$?



A work - force of 420 men with a contractor can finish a certain piece of work in 9 months. How many extra men must he employ to complete the job in 7 months ?



If the cost of $$93 m$$ of a certain kind of plastic sheet is $$Rs. 1395$$, then what would it cost to buy $$105 \ m$$ of such plastic sheet?



A car is travelling at the average speed of 50 km/hr. How much distance would it travel in 12 minutes?



Rohit bought 12 registers for Rs 156, find the cost of 7 such registers. (in Rs.)



Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job ?(in minutes)



A car can finish a certain journey in 10 hours at the speed of 48 km/hr. By how much should its speed be increased so that it may take only 8 hours to cover the same distance ? (in km/hr)



$$1200$$ men can finish a stock of food in $$35$$ days. How many more men should join them so that the same stock may last for $$25$$ days ?



55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days ?



In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last ? (in days)



Anupama takes 125 minutes in walking a distance of 100 metre. What distance would she cover in 315 minutes?



In library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 meters?



18 men can reap a filed in 35 days. For reaping the same filed in 15 days, how many men are required?



A worker is paid $$\text{Rs } 210$$ for $$6$$ days work. If his total income of the month is $$\text{Rs } 875$$, for how many days did he work?



The second class railway fare for $$240\ km$$ of journey is $$Rs. 15.00$$. What would be the fare for a journey of $$139.2\ km$$?



A worker is paid Rs 200 for 8 days work. If he works for 20 days, how much will he get?



The cost of 97 metres of cloth is $$\text{Rs }242.50$$. What length of this can be purchased for $$\text{Rs } 302.50?$$



11 men can dig $$ 6\dfrac{3}{4}$$ metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day?



In 15 days, the earth picks up $$ 1.2 \times 10^{8} $$ kg of dust from the atmosphere. In how many days it will pick up $$ 4.8 \times 10^{8}$$ kg of dust?



68 boxes of a certain commodity require a shelf-length of 13.6 m. How many boxes of the same commodity would occupy a shelf length of 20.4 m?



If the thickness of a pile of 12 cardboards is 35 mm, find the thickness of a pile of 294 cardboards.



Fill in the blanks to make the statement true:
When two quantities $$x$$ and $$y$$ are in ______ proportion or vary ______ they are written as $$x \propto y$$.



The number of people working and the quantity of work.



The price of $$3$$ metres of cloth is Rs. $$79.50$$. Find the price of $$15$$ metres of such cloth.



Simple interest on a given sum and the rate of interest.



Ram scored 553 marks out of 700 and Gita scored 486 marks out of 600 in science. Whose performance is better?



Observe the table given below and in the case find whether $$x$$ and $$y$$ are inversely proportional:
$$x$$$$5$$$$9$$$$15$$$$3$$$$45$$
$$y$$$$18$$$$10$$$$6$$$$30$$$$2$$



Number of student in a hostel and consumption of food.



The quantity of rice and its cost.



Area of the walls of a room and the cost of white washing the walls.



If $$x=5y$$, then $$x$$ and $$y$$ vary _______ with each other.



From the following table, determine if $$x$$ and $$y$$ are in direct proportion or not.
$$x$$$$1$$$$4$$$$9$$$$20$$
$$y$$$$1.5$$$$6$$$$13.5$$$$30$$



From the following table, determine if $$x$$ and $$y$$ are in direct proportion or not.
$$x$$$$4$$$$7$$$$10$$$$16$$
$$y$$$$24$$$$42$$$$60$$$$96$$



From the following table, determine if $$x$$ and $$y$$ are in direct proportion or not.
$$x$$$$3$$$$6$$$$15$$$$20$$$$30$$
$$y$$$$12$$$$24$$$$45$$$$60$$$$120$$



The height of a tree and the number of years.



Increase in cost and number of shirts that can be purchased if the budget remains the same.



Find the values of $$x$$ and $$y$$ if $$a$$ and $$b$$ are in inverse proportion:
$$305\ y$$



Area of land and its cost.



Under the condition that the temperature remains constant, the volume of gas is inversely proportional to its pressure. If the volume of gas is $$630$$ cubic centimeters at a pressure of $$360$$ mm of mercury, then what will be the pressure of the gas, if its volume is $$720$$ cubic centimeters at the same temperature?



Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.

Number of spokes4681012
Angle between a pair of consecutive spokes (in degrees)9060 .........

(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?

(ii) Calculate the angle between a pair of consecutive spokes on a wheel with $$15$$ spokes

(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is $$40$$?

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Class 8 Maths Extra Questions