JAMB 2003 · UME · Q19

Variation

$x$ varies directly as the product of $U$ and $V$ and inversely as their sum. If $x = 3$ when $U = 3$ and $V = 1$ , what is the value of $x$ if $U = 3$ and $V = 3$ ?

Worked solution (try it first)

Product on top, sum underneath: $x = \dfrac{kUV}{U + V}$ .
$x = 3$ , $U = 3$ , $V = 1$ : $3 = \dfrac{3k}{4}$ , so $k = 4$ .
$U = 3$ , $V = 3$ : $x = \dfrac{4 \times 9}{6} = 6$ , option C.

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