WAEC 2023 · Paper 1 · Q10

$M$ varies jointly as the square of $n$ and the square root of $q$ . If $M = 24$ when $n = 2$ and $q = 4$ , find $M$ when $n = 5$ and $q = 9$ .

Worked solution (try it first)

Jointly as $n^2$ and $\sqrt q$ : $M = kn^2\sqrt q$ .
Put in $M = 24$ , $n = 2$ , $q = 4$ : $24 = k \times 4 \times 2 = 8k$ , so $k = 3$ .
When $n = 5$ , $q = 9$ : $M = 3 \times 25 \times 3 = 225$ , option D.