Question

By selling an item at a discount of 20%, the profit is 20%. The profit percentage, if the item is sold at a discount of 10%, is:

• A. 30%
• B. 32%
• C. 35%
• D. 38%

Hint:

To calculate profit percentages after a discount, first find the marked price using the cost price and given profit, then apply the new discount and calculate the profit percentage.

Answer 1

The Correct Option is C

Let the cost price of the item be \( C \). Step 1: When the item is sold at a 20% discount, the selling price is \( 0.8 \times \text{marked price} \). The profit is given as 20%. So, the selling price is \( C + 0.2C = 1.2C \). Thus, the marked price \( M \) is: \[ 0.8M = 1.2C \quad \Rightarrow \quad M = \frac{1.2C}{0.8} = 1.5C. \] Hence, the marked price is \( 1.5C \). Step 2: Now, when the item is sold at a 10% discount, the selling price is \( 0.9 \times M = 0.9 \times 1.5C = 1.35C \). Step 3: The profit in this case is: \[ \text{Profit} = 1.35C - C = 0.35C. \] Thus, the profit percentage is: \[ \text{Profit Percentage} = \frac{0.35C}{C} \times 100 = 35%. \]