Question
A shopkeeper marks his goods 40% above the cost price.
He allows a discount of x% on the marked price, but while selling he uses a weight of 800 g instead of 1 kg and still makes an overall profit of 40%. Find the value of x.Solution
ATQ, Let cost price of 1 kg = Rs. 100. Then marked price (MP) of 1 kg = 100 × 1.40 = Rs. 140. He actually gives 800 g but charges for 1 kg (after discount). Selling price (SP) for 800 g = MP × (1 − x/100) = 140 × (1 − x/100). Cost price of 800 g = 100 × 0.8 = Rs. 80. Given overall profit = 40%: Profit% = [(SP − CP) / CP] × 100 = 40 ⇒ (140(1 − x/100) − 80) / 80 = 0.40 ⇒ 140(1 − x/100) − 80 = 32 ⇒ 140(1 − x/100) = 112 ⇒ 1 − x/100 = 112/140 = 0.8 ⇒ x/100 = 0.2 ⇒ x = 20.
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