Multiple choice

A retailer marked up the price of a smartwatch by 40% and gave a discount of m%. He then made a profit of (m – 8)%. If the cost price of a headphone is Rs. 250 and he gains a profit of 1.8m%, what is the selling price (in rupees) of the headphone?

  1. 340

  2. 380

  3. 430

  4. 480

  5. 570
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A Correct answer
Explanation

Let CP = 100. Marked price = 140. Selling price = 140(1 - m/100). Profit = SP - CP = 40 - 1.4m. Given profit = m - 8, so 40 - 1.4m = m - 8, which gives 2.4m = 48, so m = 20. For the headphone, CP = 250 and profit = 1.8m% = 36%. SP = 250 * 1.36 = 340.

AI explanation

Let the cost price of the smartwatch be 100; marking it up by 40% sets the marked price to 140. Applying the formula for profit percentage after discount, 140 * (1 - m/100) = 100 + (m - 8). Solving 140 - 1.4m = 92 + m gives 2.4m = 48, so m = 20. The profit percentage on the headphone is 1.8 * 20 = 36%, and applying this to the cost price of Rs. 250 gives a selling price of 250 * 1.36 = Rs. 340.

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