The marked price of a shirt is twice of the cost price. To earn a gain of 25%, what should be the discount percentage?

Options

A. 37.5
B. 50
C. 75
D. 52.5

Answer

To solve the problem step by step, we will follow these calculations:

1. **Define the Cost Price (CP)**:
Let the cost price of the shirt be \( X \).

2. **Calculate the Marked Price (MP)**:
The marked price is given as twice the cost price. Therefore,
\[ \text{Marked Price (MP)} = 2X \]

3. **Determine the Selling Price (SP) for a 25% Gain**:
To earn a gain of 25%, the selling price can be calculated as follows:
\[ \text{Selling Price (SP)} = \text{Cost Price} + 25\% \text{ of Cost Price} = X + 0.25X = 1.25X \]

4. **Calculate the Discount**:
The discount can be found by subtracting the selling price from the marked price:
\[ \text{Discount} = \text{Marked Price} - \text{Selling Price} = 2X - 1.25X = 0.75X \]

5. **Calculate the Discount Percentage**:
The discount percentage is calculated based on the marked price:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{\text{Marked Price}} \right) \times 100 = \left( \frac{0.75X}{2X} \right) \times 100 \]
Simplifying this gives:
\[ \text{Discount Percentage} = \left( \frac{0.75}{2} \right) \times 100 = 0.375 \times 100 = 37.5\% \]

Thus, the discount percentage required to earn a gain of 25% is **37.5%**.