When two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely. State whether the statement is true (T) or false (F)

Solution:

The Statement is True(T)

Consider two quantities x and y.

When x increases(↑) and if y decreases(↓) or when x decreases(↓) and if (y) increases(↑), such behaviour of two quantities indicates that they vary inversely with each other.

Inverse variation can be stated mathematically as:

x ∝ 1/y

xy = k, where k is a positive constant

✦ Try This: The following table shows the variation of two quantities x and y. The variation between x and y is inverse. Is the statement true or false?

x 24 16 12 8 4
y 2 3 4 6 12

xy = 24 × 2 = 16 × 3 = 12 × 4 = 8 × 6 = 4 × 12 = k = 48

Since

xy = k = 48 where k is a positive constant

Since the product of x and y are constant implies that x and y are in inverse proportion. The statement is therefore True.

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 55

When two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely. State whether the statement is true (T) or false (F)

Summary:

When two quantities are related in such a manner that if one increases and the other decreases, then they always vary inversely. The statement is true

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