WAEC 2022 · Paper 2 · Q7

(a)
A man purchased 180 copies of a book at ₦250.00 each. He sold $y$ copies at ₦300.00 each and the rest at a discount of 5 kobo in the Naira of the cost price. If he made a profit of ₦7,125.00, find the value of $y$ .
(b)
A trader bought $x$ bags of rice at a cost $c = 24x + 103$ and sold them at a price $s = 33x - \frac{x^2}{20}$ . (i) Find the expression for the profit. (ii) If 20 bags of rice were sold, calculate the percentage profit.

Worked solution (try it first)

(a)

Cost $= 180 \times 250 = ₦45,000$ .
A discount of 5 kobo in the naira is $5\%$ , so the rest sold at $0.95 \times 250 = ₦237.50$ each.
Sales $= 300y + 237.5(180 - y) = 62.5y + 42\,750$ .
Profit: $62.5y + 42\,750 - 45\,000 = 7125$ , so $62.5y = 9375$ and $y = 150$ .

(b)(i)

Profit $= s - c$
$= 33x - \frac{x^2}{20} - (24x + 103)$
$= 9x - \frac{x^2}{20} - 103$ .

(ii)

At $x = 20$ : cost $= 24(20) + 103 = 583$ , sales $= 660 - 20 = 640$ , profit $= 57$ .
Percentage profit $= \frac{57}{583} \times 100\%$
$\approx 9.78\%$ .

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