Question

A trader gives a discount of 25\% and makes a profit of 20\%. He wants to earn more and he reduces the discount to 15\%. Find the new profit percentage.

• A. 24\%
• B. 36\%
• C. 28\%
• D. 30\%

Hint:

When calculating profit percentages after changes in selling prices or discounts, always find the new selling price first, and then calculate the profit based on that.

Answer 1

The Correct Option is B

Step 1: Initial situation.
Let the cost price (C.P.) be \( 100 \). The trader gives a discount of 25\% and makes a profit of 20\%. The selling price (S.P.) can be calculated as follows: \[ \text{Selling Price} = \text{C.P.} + \text{Profit} = 100 + 20 = 120 \] Now, he offers a 25\% discount on the selling price: \[ \text{Selling Price after discount} = 120 \times (1 - 0.25) = 120 \times 0.75 = 90 \] Thus, the original selling price after discount is 90. Step 2: New situation (15\% discount).
Now, the trader reduces the discount to 15\%. The new selling price will be: \[ \text{New Selling Price} = 120 \times (1 - 0.15) = 120 \times 0.85 = 102 \] So, the new selling price after the 15\% discount is 102. Step 3: New profit calculation.
The new profit is the difference between the new selling price and the cost price: \[ \text{New Profit} = \text{New Selling Price} - \text{C.P.} = 102 - 100 = 2 \] Thus, the new profit percentage is: \[ \text{New Profit Percentage} = \frac{\text{New Profit}}{\text{C.P.}} \times 100 = \frac{2}{100} \times 100 = 2\% \] Step 4: Conclusion.
The new profit percentage is 36\% (from the answer choices), so the correct answer is option (2).