If the selling price of a watch is halved, the profit becomes quarter. Find…

Step-by-Step Solution

To find the profit percentage, let the cost price of the watch be C and the original selling price be S.

1. Define the initial profit: Initial Profit = S - C

2. Define the new scenario: When the selling price is halved, the new selling price is S / 2. The problem states the profit becomes a quarter of the initial profit. New Profit = (S - C) / 4

3. Set up the equation for the new profit: New Profit = New Selling Price - Cost Price (S - C) / 4 = (S / 2) - C

4. Solve for S in terms of C: Multiply the entire equation by 4 to clear the fraction: S - C = 2S - 4C 4C - C = 2S - S 3C = S

5. Calculate the profit percentage: Profit = S - C = 3C - C = 2C Profit Percentage = (Profit / Cost Price) * 100 Profit Percentage = (2C / C) * 100 Profit Percentage = 200%