A shopkeeper sells two products A and B. The cost prices of products A and B are in the ratio 4:3 respectively. Product B is sold at an 8% loss, and the total selling price of both products is Rs. 4344. If product A had also been sold at an 8% loss, its selling price would have been Rs. 2208. What is the profit percentage (x%) on product A when sold at the actual selling price?

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Accepted Answer

**Solution:**

1. Let the cost price of product A be $4y$ and product B be $3y$ as given by the ratio 4:3.

2. Since product A sold at 8% loss would have a selling price of Rs. 2208, we write:
   $$
   0.92 \times 4y = 2208
   $$
   Solving for $y$:
   $$
   4y = \frac{2208}{0.92} = 2400
   $$
   Thus, $y = 600$.

3. Cost price of product B is:
   $$
   3y = 3 \times 600 = 1800
   $$

4. Product B is sold at 8% loss, so its selling price is:
   $$
   0.92 \times 1800 = 1656
   $$

5. Total selling price of both products is Rs. 4344, so selling price of product A at profit $x\%$ is:
   $$
   4344 - 1656 = 2688
   $$

6. Profit percentage $x\%$ on product A is calculated as:
   $$
   \text{Profit} = 2688 - 2400 = 288
   $$
   $$
   x = \left( \frac{288}{2400} \right) \times 100 = 12\% 
   $$

**Answer:** 12\%

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