When two quantities are related in such a manner that, if one increases, the other also increases, then they always vary directly. 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(↑) increases or when x decreases(↓) and if (y) decreases(↓), such behaviour of two quantities indicates that they vary directly with each other.

Direct variation can be stated mathematically as:

x ∝ y

x = ky, where k is a positive constant

or

x/y = k

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

x	3	5	7	9	11
y	6	10	14	18	22

y/x = 6/3 = 10/5 = 14/7 = 18/9 = 22/11 = k = 2

Since

y/x = k = 2 where k is a positive constant = 2

Or

y = 2x

Also,

x/y = 3/6 = 5/10 = 7/14 = 9/18 = 11/22 = k = 1/2 which is a constant

Since the ratios of x/y or y/x are constant implies that x and y are in the direct proportion.

The statement is therefore true.

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 54

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

Summary:

When two quantities are related in such a manner that, if one increases, the other also increases then they always vary directly the statement is true

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