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If M varies directly as N and inversely as the root of P. Gi...

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

MN ; M1P.

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