If M varies directly as N and inversely as the root of P. Given that…

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.

Correct Answer: Option 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

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