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Xavier Aptitude Test 2013 Paper

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Question : 66 of 121

Marks: +1, -0

p and q are positive numbers such that p q = qp , and q = 9p. The value of p is

$\sqrt{9}$
$6\sqrt{9}$
$2\sqrt{9}$
$8\sqrt{9}$
$3\sqrt{9}$

Solution:

(d) Given,

p^{9}=q^{p}

(p^{9})^{1/p} = (q^{p})^{1/p}

p^{\frac{q}{p}}=q

\frac{9p}{p}=q \quad [\because q=9p]

or

p^{9}=q

.........(1)

Also

p=\frac{q}{9}

.......... (2)

Dividing equation (1) by (2), we get

p^{8}=9

or

8\sqrt{9}

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