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Inverse Variation

Direct and Inverse Variation I - Concepts

Direct Variation

Inverse Variation

Class - 8th IMO Subjects

Concept Explanation

Inverse Variation

If two quantities x and y vary with each other in such a manner that the product ab remains constant and is positive ,then we say that a and b vary inversely as each other or a varies inversely as b and b varies inversely as a. Thus, if two quantities a and b vary inversely as each other, then the product ab always remains constant .The product ab is called the constant of variation .

If two quantities a and b vary inversely to each other and if $b_1,b_2$ are the values of b corresponding to the values , $a_1,a_2$ of a respectively ,then

$a_1times b_1= constant ; (=k , say ); and; a_2 times b_2 =k$

$because; a_1b_1=a_2b_2$

$Rightarrow frac{a_1}{a_2}=frac{b_2}{b_1}$

$Rightarrow ; a_1:a_2::b_2:b_1$

Rule: if two quantities a and b vary inversely as each other , then the ratio of any two values of a is equal to the inverse ratio of the corresponding values of b.

Illustration: If 52 men can do a piece of work in 35 days , in how many days 28 men will do it ?

Solution: Suppose 28 men will do the piece of the work in x days . The given information can be exhibited in the following tabular form.

Number of men	52	28
Number of days	35	x

Clearly, we can say that less is the number of men ,more will be the number of days required to finish the work.

It is therefore , the case of inverse variation .

Ratio of Number of men = Inverse ratio of number of days

$Rightarrow ;;;;;58:28; =x; :35$

$Rightarrow ;;;;;;; frac{52}{28}=frac{x}{35}$

$Rightarrow ;;52times 35=28times x$

$Rightarrow frac{52 times 35}{28}=65$

Hence, 28 men will do the work in 65 days.

Illustration: Raghu has enough money to buy 75 machines worth Rs. 200 each. How many machines he can buy if he gets a discount of Rs. 50 on each machine?

Solution: Let x be the number of machines he can buy if he gets a discount of Rs. 50 on each machine.

This information can be formulated in the following table as follows

Number of machines	75	x
Cost of machine(in Rupees)	200	150

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Sample Questions

(More Questions for each concept available in Login)

Question : 1

If a and b vary inversely, fill in the blanks:

a	16	32	8
b	4	.........	....

4,8

2,8

2,6

6,8

Right Option : B

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Question : 2

If two quantities x and y vary inversely with each other, then _______________________
A. $frac{x}{y}$ remains constant		B. (x-y) remains constant
C. (x+y) remains constant		D. (xy) remains constant
Right Option : D
View Explanation

Question : 3

6 men can complete an assignment in 10 days. In how many days the same assignment will be completed by 20 men?
A. 4 days	B. 2 days	C. 3 days	D. 6 days
Right Option : C
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