If x and y are in direct proportion, then (x - 1) and (y - 1) are also in direct proportion. State whether the statement is true (T) or false (F)

Solution:

The Statement is False(F).

If x and y are directly proportional then,

x/y = k

But

x - 1/y - 1 ≠ k

For example if x = 2 and y = 3 then

x/y = 2/3

x - 1/y - 1 = 1/2

1/2 ≠ 2/3

In other words:

x/y ≠ (x - 1)/(y - 1)

Hence (x - 1) and (y - 1) are not in direct proportion.

✦ Try This: If x = 6 and y = 8 and they are in direct proportion then x - 1 and y - 1 are also in direct proportion.

x/y = 6/8

x - 1/y - 1 = 5/7

It is evident that

6/8 ≠ 5/7

Hence

(x - 1)/(y - 1) ≠ x/y ≠ k

Therefore we can conclude that

(x - 1)/(y - 1) and x/y are not in direct proportion with each other.

The statement is False(F)

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 50

If x and y are in direct proportion, then (x - 1) and (y - 1) are also in direct proportion. State whether the statement is true (T) or false (F)

Summary:

“ If x and y are in direct proportion, then (x - 1) and (y - 1) are also in direct Proportion” is a false statement

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