A shopkeeper marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides this he also cheats both his supplier and his buyer by 100 grams while buying and selling 1 kilogram. If it is known that the shopkeeper takes a discount of 10% from his supplier and he disregards this discount while marking up (i.e he marked up on the discounted price), find the percentage profit for the shopkeeper?

Let cost price per kg = 100. Supplier gives 10% discount: shopkeeper pays 90. But shopkeeper cheats while buying - gets 1.1kg. Effective cost per kg = 90/1.1 = 81.82. Shopkeeper disregards supplier discount while marking up - marks up 100 (not 90) by 20% to 120, then gives 10% discount: 120 × 0.9 = 108. Cheats while selling - gives only 0.9kg. Effective selling price = 108/0.9 = 120. Profit = (120 - 81.82)/81.82 = 46.66%. Key insight: marking up on undiscounted price despite receiving discount.