If p and q are in inverse variation then (p + 2) and (q - 2) are also in inverse proportion. State whether the statement is true (T) or false (F)

Solution:

The statement is False(F)

If p and q are in in inverse variation then

p ∝ 1/q

pq = constant = k

However,

(p + 2)(q - 2) ≠ k

Therefore (p + 2) and (p - 2) are not in inverse variation or proportion

✦ Try This: If p = 10 and q = 5 are in inverse variation then (p + 2) and (q - 2) are also in inverse proportion.

If p = 10 and q = 5

Then,

p + 2 = 10 + 2 = 12

q - 2 = 5 - 2 = 3

If p and q are in inverse variation the

pq = k = positive constant

pq = 10 × 5 = 50

Similarly if (p + 2) and (q - 2) are in inverse variation then

(p + 2)(q - 2) = 12 × 3 = 36

Hence we conclude that,

(p + 2)(q - 2) ≠ pq

Because

36 ≠ 50

Hence (p + 2) and (q - 2) are not in inverse variation.

The statement is therefore False(F)

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 52

If p and q are in inverse variation then (p + 2) and (q - 2) are also in inverse proportion. State whether the statement is true (T) or false (F)

Summary:

If p and q are in inverse variation then (p + 2) and (q - 2) are also in inverse proportion. The statement is False(F)

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