JAMB 1987 · UME · Q19

If $P$ varies inversely as $V$ and $V$ varies directly as $R^2$ , find the relationship between $P$ and $R$ , given that $R = 7$ when $P = 2$ .

Worked solution (try it first)

$P = \dfrac{c}{V}$ and $V = mR^2$ , so $P = \dfrac{c}{mR^2}$ : $P$ varies inversely as $R^2$ .
So $P = \dfrac{k}{R^2}$ , which means $PR^2 = k$ .
Put in $R = 7$ , $P = 2$ : $k = 2 \times 49 = 98$ .
So $PR^2 = 98$ , option B.