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JAMB Mathematics 2014 Paper

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Question : 14

Total: 47

P varies directly as Q and inversely as R. When Q = 36 and R = 16, P = 27. Find the relation between P, Q and R.

$P = \frac{Q}{12R}$
$P = \frac{12Q}{R}$
$P = 12QR$
$P = \frac{12}{QR}$

Solution:

Concept:

Combined variation uses a constant

k

to relate direct and inverse proportionality in one equation.

Explanation:

Since

P

varies directly as

Q

and inversely as

R

, write:

P = k \cdot \frac{Q}{R}

Substitute

Q = 36

,

R = 16

, and

P = 27

:

27 = k \cdot \frac{36}{16}

Simplify the fraction:

27 = k \cdot \frac{9}{4}

Solve for

k

:

k = 27 \times \frac{4}{9} = 12

Therefore, the relation is:

P = \frac{12Q}{R}

Answer:

P = \frac{12Q}{R}

(Option B).

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