Theory question 112
Commercial Arithmetic(a) A shop-owner marked a shirt at a price to enable him make a gain of 20%. During a special sales period, the shirt was sold at 10% reduction to a customer for N864.00. What was the original cost to the shop-owner?
(b) A rectangular lawn of length (x + 5) metres is (x − 2) metres wide. If the diagonal is (x + 6) metres, find; (i) the value of x (ii) the area of the lawn.
Show the model answer
Model answer
(a) Marked price = 1.2C; sale price = 0.9 × 1.2C = 1.08C = 864, so C = N800.00.
(b)(i) (x + 5)2 + (x − 2)2 = (x + 6)2 gives x2 − 6x − 7 = 0, (x − 7)(x + 1) = 0, so x = 7 (x = −1 makes the width negative).
(ii) Length 12 m, width 5 m: area = 60 m2.
Explanation
Work back from the sale price: each percentage change multiplies the price.