A dishonest dealer defrauds to the extent of x% in buying as well as selling his goods by using faulty weight. What will be the gain percent on his outly?

Options

A. `(2x+(x^2/100))`%
B. `((10/x)+x^2)`%
C. `(x^2/100)`%
D. `(2x-(x^2/100))`%

Answer

To solve the problem of a dishonest dealer who defrauds by x% in both buying and selling, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
The dealer cheats by x% while buying and x% while selling. We need to find the overall gain percentage on his outlay.

2. **Calculating the Effective Gain**:
When the dealer buys goods, he pays for only (100 - x)% of the actual value. This means if the cost price (CP) is 100 units, he effectively pays:
\[ \text{Effective CP} = 100 - x \]

3. **Selling Price Calculation**:
When he sells the goods, he sells them at (100 + x)% of the cost price. Therefore, the selling price (SP) becomes:
\[ \text{SP} = 100 + x \]

4. **Finding the Gain**:
The gain can be calculated as:
\[ \text{Gain} = \text{SP} - \text{Effective CP} \]
Substituting the values we found:
\[ \text{Gain} = (100 + x) - (100 - x) = 100 + x - 100 + x = 2x \]

5. **Calculating Gain Percentage**:
The gain percentage is calculated based on the effective cost price:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{Effective CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left(\frac{2x}{100 - x}\right) \times 100 \]

6. **Final Formula**:
Simplifying the expression gives us:
\[ \text{Gain Percentage} = \frac{200x}{100 - x} \]

### Conclusion:
The gain percentage on the outlay for a dishonest dealer who cheats by x% in both buying and selling is given by:
\[ \text{Gain Percentage} = \frac{200x}{100 - x} \]