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

Solution:

The Statement is False(F).

If x and y are in inverse proportion then,

x ∝ 1/y

x = k/y

xy = k

If xy = k then

(x + 1)(y + 1) ≠ xy

For x +1 and y + 1 to be in proportion :

(x + 1)/(y + 1) = xy

But that is not the case. Hence

(x + 1) and (y+1) are not in inverse proportion.

For example if x = 2 and y = 3 then

xy = 2 × 3 = 6

(x + 1)(y + 2)= (3)(4) = 12

6 ≠ 12

In other words:

xy ≠ (x + 1)/(y + 1)

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

✦ Try This: If x = 3 and y = 5 and they are in inverse proportion then x + 1 and y + 1 are also in inverse proportion.

xy = 3 × 5 = 18

(x + 1)/(y + 1) = (3 + 1)(5 + 1) = (4)(6) = 24

It is evident that

18 ≠ 24

Hence

(x + 1)/(y + 1) ≠ xy ≠ k

Therefore we can conclude that

(x + 1) and (y + 1) are not in inverse proportion.

The statement is False(F)

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 51

If x and y are in inverse proportion, then (x + 1) and (y + 1) are also in inverse 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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