p varies directly as the square of q and inversely as r. If p = 36, when q = 3, when r = 4, find p when q = 5 and r = 2.
A
72
B
100
C
90
D
200
E
125
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
P \(\alpha\) \(\frac{q^2}{r}\)
P = \(\frac{kq^2}{r}\)
k = \(\frac{pr}{q^2}\)
= \(\frac{36 x 4}{(3)^2}\)
p = \(\frac{16q^2}{r}\)
= \(\frac{16 \times 25}{2}\)
= 200
Source: Myschool Past Questions Archive (Record #32350)