Question

7(a) A man purchased 180 copies of a book at N250.00 each. He sold y copies at N300.00 each and the rest at a discount of 5 kobo in the Naira of the cost price. If he made a profit of N7,125.00, 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−x²/20.
(i) Find the expression for the profit.
(ii) If 20 bags of rice were sold, calculate the percentage profit.

Accepted Answer

(a) Total cost of 180 copies, C.P = 180×250 = N45,000.
Selling price for y copies = y×300 = N300y.
After selling y copies, remaining copies = (180−y).
5% discount means selling at: (100−5)/100 × S.P = 95/100 × 250
Thus, S.P for the remaining copies = (180−y)×237.5 = 42,750−237.5y
Total S.P = 300y+42,750−237.5y
Profit = S.P − C.P
7,125 = 62.5y+42,750−45,000
7,125 = 62.5y−2,250
y = 9,375/62.5 = 150.

(b)(i) Profit = s−c = (33x−x²/20)−(24x+103) = 9x−x²/20−103.

(ii) With x=20 bags: Cost = 24(20)+103 = 583.00. Selling price = 33(20)−20²/20 = 660−20 = 640.
%profit = (S.P−C.P)/C.P × 100% = (640−583)/583 × 100% = 9.78%.

WAEC Mathematics 2022 Theory — Question 7

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