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Inverse Variation

Direct and Inverse Variation I - Concepts

Direct Variation

Inverse Variation

Class - 8th DAV 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

Amar takes 15 days to reduce 20 kilograms of his weight by doing 20 minutes of exercise per day. If he does exercise for 1 hour per day, how many days will he take to reduce the same weight?
A. 5 DAYS	B. 1 DAY	C. 9 DAYS	D. 4 DAYS
Right Option : A
View Explanation

Question : 2

40 labourers can build a house in 40 days. How many labourers should be engaged by the contractor to complete the work in 50 days?
A. 30 labourers	B. 33 labourers	C. 32 labourers	D. 35 labourers
Right Option : C
View Explanation

Question : 3

30 men can finish a work in 28 days. How much time will be taken by 21 men, to finish the same work ?
A. 30 days	B. 33 days	C. 38 days	D. 40 days
Right Option : D
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