A dealer bought an article at 10% discount on its marked price , and sold at a price which was 15% above the marked price. The gain per cent ( correct to the nearest integer) is :

Options

A. 0.33
B. 0.35
C. 0.25
D. 0.28

Answer

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

1. **Understanding the Cost Price (CP)**:
- The dealer bought the article at a 10% discount on its marked price (MP).
- Therefore, the cost price (CP) can be calculated as:
\[ CP = MP - (10\% \text{ of } MP) = MP - 0.10 \times MP = 0.90 \times MP \]

2. **Calculating the Selling Price (SP)**:
- The dealer sold the article at a price which was 15% above the marked price.
- Therefore, the selling price (SP) can be calculated as:
\[ SP = MP + (15\% \text{ of } MP) = MP + 0.15 \times MP = 1.15 \times MP \]

3. **Calculating the Gain**:
- The gain can be calculated as:
\[ \text{Gain} = SP - CP = (1.15 \times MP) - (0.90 \times MP) = 0.25 \times MP \]

4. **Calculating the Gain Percentage**:
- The gain percentage is given by the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{CP} \right) \times 100 \]
- Substituting the values we calculated:
\[ \text{Gain Percentage} = \left( \frac{0.25 \times MP}{0.90 \times MP} \right) \times 100 \]
- The \( MP \) cancels out:
\[ \text{Gain Percentage} = \left( \frac{0.25}{0.90} \right) \times 100 \]
- Simplifying this:
\[ \text{Gain Percentage} = \frac{25}{9} \approx 2.777 \times 100 \approx 27.777\% \]

5. **Rounding to the Nearest Integer**:
- Rounding 27.777 to the nearest integer gives us 28%.

Thus, the gain percentage, correct to the nearest integer, is **28%**.