JAMB 1984 · UME · Q5

Quadratics & their graphs
Commercial arithmetic

If the price of oranges is raised by $\frac12$ k per orange, the number of oranges a customer can buy for ₦2.40 will be less by 16. What is the present price of an orange?

Worked solution (try it first)

Work in kobo: ₦2.40 is 240k.
With a price of $p$ kobo you buy $\frac{240}{p}$ oranges now and $\frac{240}{p + \frac12}$ after the rise.
The difference is 16: $\dfrac{240}{p} - \dfrac{240}{p + \frac12} = 16$ .
Multiply by $p(p + \frac12)$ : $120 = 16p^2 + 8p$ .
Divide by 8 and rearrange: $2p^2 + p - 15 = 0$ , which factorises as $(2p - 5)(p + 3) = 0$ .
A price is positive, so $p = \frac52$ .
An orange costs $2\frac12$ k now, option A.

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