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CBSE Questions for Class 8 Maths Direct And Inverse Proportions Quiz 1 - MCQExams.com
CBSE
Class 8 Maths
Direct And Inverse Proportions
Quiz 1
Which is an example of inverse proportion?
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More amount of sweets, more total cost
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More length of cloth, more cost
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More expenditure, less saving
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More height of object, more length of its shadow
Explanation
2 quantities say it be $$x , y$$ are said to be in proportion when the change in value of $$x$$ , leads to the equal change in value of $$y$$.
If $$x$$ increases and hence $$y$$ decreases proportionally, it is called Inverse proportion i.e $$x\propto\dfrac{1}{y}$$
For example, In option C, if our expenses are more, then we are left with lesser savings from a fixed salary or income.
hence, Expenditure and savings are in inverse proportion.
So the answer is C
Which is example of inverse proportion?
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Length of edge of square & its area
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Speed and time taken
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Length of edge of square & its perimeter
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Quantity of pencils & total cost
Explanation
2 quantities say it be $$x , y$$ are said to be in inverse proportion when the increse in value of $$x$$ , leads to the decrease in value of $$y$$.
we know that,
$$speed = \dfrac{distance}{time}$$
i.e., Speed is directly proportion to distance and at a fixed distance inverse proportion to time.
Hence at fixed distance, if speed increses, time taken will decrease and vice versa. which is Option B
Which of the following are in inverse proportion?
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The number of workers on a job and the time to complete the job.
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The time taken for a journey and the distance travelled in a uniform speed.
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Area of cultivated land and the crop harvested.
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The time taken for a fixed journey and the speed of the vehicle.
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The population of a country and the area of land per person.
Explanation
Inverse proportion is a relation between two quantities such that one increases in proportion as the other decreases i.e. If $$x$$ increases as $$y$$ decreases, $$x \alpha \dfrac{1}{y}$$
In option A, if the no. of workers are increased then the time required to do the job will decrease, likewise if no. of workers decrease, then time to do the same job will increase i.e. no. of workers and time to do the job are inversely proportional to each other.
Similarly is the option D and E where the time taken to complete the journey is inversely proportional to the speed of vehicle and population is inversely proportional to area of the land respectively, are both examples of inverse proportion.
So, the answer is A, D, E.
Cost of 10 mangoes is Rs.The cost of 18 mangoes is__
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Rs. 18
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Rs. 108
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Rs. 200
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Rs. 180
Explanation
Here, the cost of mangoes is directly proportional to the number of mangoes bought.
So, if $$ 10 $$ mangoes costs $$ Rs.\ 100 $$, then $$ 1 $$ mango will cost $$ Rs. \dfrac{ 100 }{10} = Rs . 10 $$
Therefore, $$ 18 $$ mangoes will cost $$= 18 \times \dfrac{ 100 }{10} = Rs. 180 $$
State true or false:
Following are the car parking charges near a railway station upto
4 hours Rs 60
8 hours Rs 100
12 hours Rs 140
24 hours Rs 180
Hence, the parking charges are in direct proportion to the parking time.
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True
0%
False
Explanation
Suppose time is denoted by $$x$$ and parking charge is denoted by $$y$$.
For $$x=4 hours$$, $$y=60 Rs$$. Therefore, $$\dfrac{x}{y}=\dfrac{4}{60} = \dfrac{1}{15}$$
For $$x=8 hours$$, $$y=100 Rs$$. Therefore, $$\dfrac{x}{y}=\dfrac{8}{100} = \dfrac{2}{25}$$
For $$x=12 hours$$, $$y=140 Rs$$. Therefore, $$\dfrac{x}{y}=\dfrac{12}{140} = \dfrac{3}{35}$$
For $$x=24 hours$$, $$y=180 Rs$$. Therefore, $$\dfrac{x}{y}=\dfrac{24}{180} = \dfrac{2}{15}$$
Since, ratio of $$x$$ and $$y$$ is different for each time period, parking charges are not directly proportional to parking time.
Eight oranges can be bought for Rs $$10.40$$, then how many more oranges can be bought for Rs $$16.90$$?
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$$5$$ oranges
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$$3$$ oranges
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$$7$$ oranges
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$$2$$ oranges
Explanation
Let $$x$$
oranges be bought for
Rs.
$$ 16.90.$$
Given, eight oranges are bought for
Rs.
$$ 10.40.$$
Then, $$\dfrac{8}{x}=\dfrac{10.40}{16.90}$$
$$\Longrightarrow x=\dfrac{16.90\times 8}{10.40}=13$$
Then, $$(13-8)=5$$
more oranges can be bought.
If $$a : b = 5 : 9$$ and $$b : c = 4 : 7$$ find $$a : b : c$$
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$$5:9:\dfrac{63}{4}$$
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$$20:63:36$$
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$$4:36:63$$
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$$20:36:63$$
Explanation
Given, $$a : b = 5 : 9 $$ and $$b : c = 4 : 7$$ $$=$$ $$\displaystyle \left ( 4\times
\frac{9}{4} \right ):\left ( 7\times \frac{9}{4} \right
)=9:\frac{63}{4}$$
$$\displaystyle \Rightarrow a:b:c=5:9:\frac{63}{4}=20:36:63$$
$$ x$$
$$2$$
$$ 5$$
$$ 25$$
$$ y$$
$$25$$
$$10$$
$$m$$
If $$x$$ & $$y$$ are in inverse proportion, find m
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$$1$$
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$$2$$
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$$3$$
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$$4$$
Explanation
The given example is of inverse proportion.
by definition,
$$x\propto \dfrac{1}{y}$$ i.e. $$x = K\dfrac{1}{y}$$ , where $$K$$ is constant of proportionality
$$\therefore xy = K$$
$$x\times y = 2\times 25 = 50 = K$$
now, $$25\times m = 50$$
$$\therefore m = 2$$
Answer is option B
Find the value of $$x$$ if $$a$$ and $$ b$$ are in direct proportion
$$a$$
$$2$$
$$3$$
$$4$$
$$5$$
$$b$$
$$14$$
$$21$$
$$x$$
$$35$$
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$$16$$
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$$25$$
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$$27$$
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$$28$$
Explanation
$$a$$ and $$b$$ are in direct proportion
$$\therefore \dfrac {a}{b} = k = \dfrac {2}{14} = \dfrac {3}{21} = \dfrac {1}{7}$$
$$\therefore \dfrac {4}{x} = \dfrac {1}{7} \Rightarrow x = 28$$.
If x & y are in direct proportion then find the value of a
x
2
3
5
7
y
4
6
a
14
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$$8$$
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$$10$$
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$$15$$
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$$20$$
Explanation
We know that, in direct proportion, the ratio of the quantities remains constant
$$\therefore \ \dfrac{x}{y}=k$$
$$\dfrac{2}{4}=\dfrac{3}{6}=\dfrac{5}{a}=\dfrac{7}{14}=k\;\Rightarrow\;k=\dfrac{1}{2}=\dfrac{5}{a}\;\Rightarrow\;a=10$$
Thus option B is the correct answer.
If $$x$$ & $$y$$ are in inverse proportion then find proportionality constant at $$x=3,\;y=2$$
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$$4$$
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$$5$$
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$$6$$
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$$7$$
Explanation
Given that. $$x$$ and $$y$$ are inverse proportion,
i.e. $$x \propto \dfrac{1}{y}$$
$$\therefore xy = K$$, where $$K$$ is constant proportionality
Given.
$$x = 3, y = 2$$
$$\therefore 3\times2 = K = 6$$
Answer is $$6$$
$$x$$
$$2$$
$$ 3$$
$$ 5$$
$$ 6$$
$$10$$
$$ y$$
$$15$$
$$10$$
$$ b$$
$$5$$
$$ 3$$
Identify the inverse proportional quantities.
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$$4$$
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$$5$$
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$$6$$
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$$10$$
Explanation
The given example is of inverse proportion.
by definition,
$$x\propto \dfrac{1}{y}$$ i.e. $$x = K\dfrac{1}{y}$$ , where $$K$$ is constant of proportionality
$$\therefore xy = K$$
$$x\times y = 2\times 15 = 30 = K$$
now, $$5\times b = 30$$
$$\therefore b = 6$$
Answer is option C
$$14$$ apples cost $$Rs. 140.$$ Then, the cost of 1 apple is__
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$$Rs. 10$$
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$$Rs. 8$$
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$$Rs. 4$$
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$$Rs. 14$$
Explanation
The cost of apples is directly proportional to the number of apples bought.
So, if $$ 14 $$ apples cost $$ Rs\ 140 $$, then $$ 1 $$ apple will cost $$ Rs \dfrac{ 140 }{14} = Rs 10 $$
Find inverse proportionaly constant if $$x$$ and $$y$$ are in inverse proportion.
$$x$$
$$9$$
$$6$$
$$3$$
$$18$$
$$y$$
$$2$$
$$3$$
$$6$$
$$1$$
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$$9$$
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$$18$$
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$$27$$
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$$30$$
Explanation
$$\because x$$ and $$y$$ are inverse porportion
$$\therefore x \times y = k \Rightarrow 9\times 2 = 6\times 3 = 3\times 6 = 18\times 1 = 18 = k$$
The cost of $$2$$ meter cloth is $$10$$. Find the cost of $$100\ m$$ cloth.
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$$400$$
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$$500$$
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$$1000$$
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$$1500$$
Explanation
Cost of cloth is directly proportional to its length.
$$10 = 2\times k \Rightarrow k = 5$$ , where k is the cost of cloth per meter
$$\therefore$$ Cost of $$100\ m$$ cloth $$=5\times 100 = 500$$.
Which of the following $$a$$ & $$b$$ are in direct proportion?
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$$a=\dfrac{2}{b}$$
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$$a=2b$$
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$$a=b^3$$
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$$a=\dfrac{1}{b^2}$$
Explanation
If two numbers $$a$$ and $$b$$ are in direct proprtion then $$\dfrac{a}{b}=\text{ constant}$$
From option (B), $$\dfrac{a}{b}=2$$
$$\implies \dfrac{a}{b}=\text{ constant}$$ $$[\because 2$$ is a constant number $$]$$
Hence, option (B) is correct
$$a$$ and $$b$$ are in ............ proportion
$$a$$
$$3$$
$$7$$
$$10$$
$$11$$
$$b$$
$$9$$
$$21$$
$$30$$
$$33$$
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direct
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indirect
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both
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none
Explanation
$$\dfrac {a}{b} = \dfrac {3}{9} = \dfrac {7}{21} = \dfrac {10}{30} = \dfrac {11}{33} = \dfrac {1}{3} = k$$
$$\therefore a$$ and $$b$$ are in direct proportion.
If $$4$$ men earn Rs $$360$$ in one day, then how much does a man earn in one day?
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$$90$$
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$$30$$
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$$120$$
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$$60$$
Explanation
Earning of $$4$$ men $$=$$ Rs $$360$$ per day
Earning of $$1$$ man $$=$$ Rs $$\dfrac{360}{4}$$ per day
$$=$$ Rs $$90$$ per day
Which of the following is an example of indirect proportion?
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Number of mangoes in a bag and weight of the bag.
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Earning and hours worked.
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More the speed, lesser the time taken.
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None of these.
Explanation
Indirect proportion: When one quantity increases another quantity decreases.
In option C, if the speed of the vehicle increases then the time taken by it to cover a distance, decreases.
In shelf, the book with green cover and that with brown cover are in the ratio $$2 : 3$$ there are $$18$$ books with green cover, then the number of books with brown cover is ?
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$$12$$
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$$24$$
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$$27$$
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$$36$$
Explanation
Given ratio of books with green cover and brown cover $$=2: 3$$
Let the number of books with green cover be $$2 x$$
Number of books with brown cover be $$3 x$$
Given number of books with green cover $$=18$$
$$\Rightarrow 2 x=18$$
$$\therefore x=9$$
So, number of books with brown cover $$=3 x$$
$$\begin{aligned}&=3 \times 9 \\&=27\end{aligned}$$
$$\begin{aligned} \therefore \text { Number of books with brown cover }=27 \end{aligned}$$
$$\therefore \textbf{Option C is correct}$$
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