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Two quantities are said to vary ______ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant

Solution:

Consider the following table where as x increases y decreases. The value of the xy is determined as follows.

x	0.002	0.004	0.008	0.016	0.05
y	500	250	125	62.5	31.25

To verify that relationship between x and y is inversely proportion the value of k has to be ascertained

xy = k

xy = 0.002 × 500 = 0.004 × 250 = 0.016 × 62.5 = 0.05 × 31.25 = 1 = k

Since k is a constant equal to 1 we can state that x and y are inversely proportional.

Let us take another example below:

x	18	12	9	6	4
y	2	3	4	6	9

To verify that relationship between x and y is inversely proportion the value of k has to be ascertained

xy = k

xy = 18 × 2 = 12 × 3 = 9 × 4 = 6 × 6 = 4 × 9 = 36 = k

Since k is a constant equal to 36, we can state that x and y are inversely proportional.

✦ Try This: What is the value of the constant of proportionality between the two variables p and q?

p	42	28	21	14	12
q	2	3	4	6	7

p/q = 42/2 ≠ 28/3 ≠ 21/4 ≠ 14/6 ≠ 12/7 ≠ k

pq = 42 × 2 = 28 × 3 = 21 × 4 = 14 × 6 = 12 × 7 = 84 = k

Hence variables p and q are inversely proportional.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 24

Two quantities are said to vary ______ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant

Summary:

Two quantities are said to vary inversely with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remain constant

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