Question

(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-x^2/20.
(i) Find the expression for the profit.
(ii) If 20 bags of rice were sold, calculate the percentage profit.

Accepted Answer

(a) Total cost price = 250 x 180 = #45,000.
Revenue from y copies at #300 = 300y.
Remaining (180-y) copies sold at a discount of 5 kobo per Naira of cost price, i.e. at 95% of #250 = #237.50 each: revenue = 237.5(180-y).
Total revenue = 300y + 237.5(180-y) = 300y + 42,750 - 237.5y = 62.5y + 42,750.
Profit = Total revenue - Total cost = (62.5y+42,750) - 45,000 = 62.5y - 2,250 = 7,125 (given).
62.5y = 9,375, so y = 150.

(b)(i) Profit P = Selling price - Cost price = s - c = (33x - x^2/20) - (24x+103) = 9x - x^2/20 - 103.

(ii) At x=20: Cost price c = 24(20)+103 = 583.
Profit = 9(20) - (20^2)/20 - 103 = 180 - 20 - 103 = 57.
%Profit = (Profit/Cost price) x 100% = (57/583) x 100% = 9.78% (to 2 d.p.).

NECO Mathematics 2022 Theory — Question 7

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