If M varies directly as N and inversely as the root of P. Given that M = 3, N = 5 and P = 25. Find the value of P when M = 2 and N = 6.

A.

36

B.

63

C.

47

D.

81

Correct answer is D

\(M \propto N \) ; \(M \propto \frac{1}{\sqrt{P}}\).

\(\therefore M \propto \frac{N}{\sqrt{P}}\)

\(M = \frac{k N}{\sqrt{P}}\)

when M = 3, N = 5 and P = 25;

\(3 = \frac{5k}{\sqrt{25}}\)

\(k = 3\)

\(M = \frac{3N}{\sqrt{P}}\)

when M = 2 and N = 6,

\(2 = \frac{3(6)}{\sqrt{P}} \implies \sqrt{P} = \frac{18}{2}\)

\(\sqrt{P} = 9 \implies P = 9^2\)

P = 81