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: D
Explanation
\(M \propto N \) ; \(M \propto \frac{1}{\sqrt{P}}\). \(\therefore M \propto \frac{N}{\sqrt{P}}\) \(M = \frac{k N}{\sqrt{P}}\) 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