JAMB 1983 · UME · Q6

Variation

If $x$ is jointly proportional to the cube of $y$ and the fourth power of $z$ , in what ratio is $x$ increased or decreased when $y$ is halved and $z$ is doubled?

Worked solution (try it first)

Jointly proportional means $x = ky^3z^4$ .
Halving $y$ multiplies $y^3$ by $\left(\frac12\right)^3 = \frac18$ .
Doubling $z$ multiplies $z^4$ by $2^4 = 16$ .
So $x$ is multiplied by $\frac18 \times 16 = 2$ : a $2 : 1$ increase, option B.

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