A dishonest shopkeeper, at the time of selling and purchasing, weighs 20% less and 24% more per kg respectively. Find the percentage profit earned by treachery. (Assuming he sells at cost price)?

While purchasing, he gets 20% less: receives 0.8 units but pays for 1. Effective purchase price = 1/0.8 = 1.25 per unit. While selling, he gives 24% more: gives 1.24 units but charges for 1. Effective selling price = 1/1.24 per unit. But he sells at cost price, so CP = SP. Profit = (1.25 - 1/1.24) / (1/1.24) = 1.25 × 1.24 - 1 = 0.55 = 55%.