If a discount of 10% is given to a customer on the marked price of an article, the gain of the trader is 20%. What will be the gain per cent of the trader if the discount is increased to 15%?

Options

A. 12 `1/2` %
B. 13 `1/3` %
C. 14 `1/4` %
D. 15 `1/5` %

Answer

To solve the problem, we will use the relationship between discount, cost price, and selling price to find the gain percentage when the discount is increased to 15%.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- Let the marked price (MP) of the article be \( M \).
- A discount of 10% is given, so the selling price (SP) after the discount is:
\[ SP = M - 0.10M = 0.90M \]
- The gain of the trader with a 10% discount is 20%. This means:
\[ SP = CP + 0.20CP = 1.20CP \]
- Therefore, we can equate the two expressions for SP:
\[ 0.90M = 1.20CP \]

2. **Finding the Relationship Between CP and M:**
- Rearranging the equation gives:
\[ CP = \frac{0.90M}{1.20} \]
- Simplifying this:
\[ CP = 0.75M \]

3. **Calculating the Selling Price with a 15% Discount:**
- Now, if the discount is increased to 15%, the new selling price is:
\[ SP = M - 0.15M = 0.85M \]

4. **Finding the New Gain Percentage:**
- We know the cost price (CP) is \( 0.75M \). The new gain can be calculated as:
\[ \text{Gain} = SP - CP = 0.85M - 0.75M = 0.10M \]
- To find the gain percentage:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{CP}\right) \times 100 = \left(\frac{0.10M}{0.75M}\right) \times 100 \]
- Simplifying this:
\[ \text{Gain Percentage} = \left(\frac{0.10}{0.75}\right) \times 100 = \left(\frac{10}{75}\right) \times 100 = \frac{1000}{75} \approx 13.33\% \]

5. **Conclusion:**
- Therefore, the gain percentage of the trader when the discount is increased to 15% is approximately **13.33%**.