A trader by mean of a false balance defrauds to the extent of `8%` in buying goods and also defrauds to `8%` in selling. His gain per cent is-

Options

A. `15.48%`
B. `16%`
C. `16.64%`
D. None of these

Answer

To solve the problem of a trader who defrauds by 8% in both buying and selling, we can use the formula for calculating the overall gain percentage when there are two successive percentages involved.

### Step-by-Step Solution:

1. **Understand the Problem**: The trader defrauds by 8% while buying and 8% while selling. We need to find the overall gain percentage.

2. **Identify the Formula**: The formula to calculate the overall gain percentage when there are two successive percentages is:
\[ \text{Gain Percentage} = \frac{(100 + x)(100 + y) - 10000}{100} \]
where \(x\) and \(y\) are the gain percentages in buying and selling, respectively.

3. **Substitute the Values**: Here, both \(x\) and \(y\) are 8%. So we substitute \(x = 8\) and \(y = 8\) into the formula:
\[ \text{Gain Percentage} = \frac{(100 + 8)(100 + 8) - 10000}{100} \]

4. **Calculate the Values**:
- First, calculate \(100 + 8 = 108\).
- Now, calculate \(108 \times 108 = 11664\).
- Next, subtract 10000 from 11664:
\[ 11664 - 10000 = 1664 \]
- Finally, divide by 100:
\[ \text{Gain Percentage} = \frac{1664}{100} = 16.64\% \]

5. **Conclusion**: The overall gain percentage of the trader is **16.64%**.