A shopkeeper marks the price of his goods at 50% above the cost price. He offers a discount of x% on the marked price, but he also gives 10% less quantity than what he claims (i.e., he gives 900 g instead of 1 kg when selling “1 kg”). If his overall profit percentage (on actual cost price) is 40%, what is the value of x?

Assume cost price (CP) of 1 kg of the commodity = Rs 100. Marked price (MP) = 50% above CP = 100 × 1.5 = Rs 150 He claims to sell 1 kg but gives only 900 g = 0.9 kg. Selling price (SP) of “1 kg (claimed)” after x% discount: = MP × (1 − x/100) = 150(1 − x/100) This is the amount received for 0.9 kg of goods. So SP per kg actually = [150(1 − x/100)] / 0.9 Profit% = 40% on cost price of Rs 100 ⇒ SP per kg must be Rs 140 Thus: [150(1 − x/100)] / 0.9 = 140 150 / 0.9 = 150 × (10/9) = 1500/9 = 500/3 So: (500/3)(1 − x/100) = 140 1 − x/100 = 140 × 3 / 500 = 420 / 500 = 0.84 ⇒ x/100 = 1 − 0.84 = 0.16 ⇒ x = 16 So the required discount = 16%.