UPSC CDS 2 2021 Math Paper

Given, p varies directly as q and inversely as square of r.
Hence, ‌‌p=‌

q

r2

, Assuming proportional constant as 1.
q is increased by 20% and r is decreased by 20%.
Hence, value of p becomes,
‌p=‌

1.20q

(8r)2

‌p=‌

120q

64r2

Change in value of p=‌

120q

64r2

−‌

q

r2

=‌

56

64

⋅‌

q

r2

Increase in P's percentage
‌‌=‌

( 56 64 ⋅ q r2 )

(‌ q r2 )

×100
‌‌=‌

56

64

×100
‌‌=‌

7

8

×100
‌‌=‌

700

8

=87.5%
Hence, percentage increase in p is 87.5%.