A man purchased some watches at Rs. 400 per watch. He sold (2/5) of them at a 20% profit. If, upon selling all the watches, he earns an overall profit of 12%, then at what price per watch should he sell the remaining watches?

Let the total number of watches purchased be x . Cost price of each watch = Rs. 400 Total cost price = 400 × x = 400x He sold (2/5) of the watches at a 20% profit. Number of watches sold at 20% profit = (2/5) × x = (2x/5) Selling price of these watches = (2x/5) × 400 × 1.20 = (2x/5) × 480 = 960x/5 = 192x For the remaining (3/5) × x = (3x/5) watches, let the price per watch at which they are sold be y . Thus, selling price of the remaining watches = (3x/5) × y According to the overall profit of 12%, the total selling price should be: Total selling price = 400x × 1.12 = 448x Now, the total selling price is the sum of the selling prices of both parts: 192x + (3x/5) × y = 448x Solve for y: (3x/5) × y = 448x - 192x = 256x y = (256x × 5) / (3x) = 1280 / 3 = Rs. 426.67 Thus, the remaining watches should be sold at Rs. 426.67 per watch to achieve an overall profit of 12%. Correct answer: (b) Rs. 426.67 .