A shopkeeper cheats to the extent of 21 % while buying and selling fruits, by using tampered weights His total gain ( in percentages: )

Options

A. 46.41
B. 46.25
C. 46.75
D. 46.5

Answer

To solve the problem of the shopkeeper's total gain percentage when he cheats by 21% while buying and selling fruits, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Cheating Percentage**:
The shopkeeper cheats by 21%. This means when he buys fruits, he gets 21% more than what he actually pays for.

2. **Calculating the Effective Quantity Bought**:
Let's assume the shopkeeper buys 100 fruits.
Since he cheats by 21%, he effectively gets:
\[ \text{Effective Quantity} = 100 + 21\% \text{ of } 100 = 100 + 21 = 121 \text{ fruits} \]

3. **Calculating the Selling Price**:
When selling, he again cheats by 21%. The selling price (SP) will be based on the effective quantity he has, which is 121 fruits.
The selling price can be calculated as:
\[ \text{SP} = \text{CP} + 21\% \text{ of } \text{CP} \]
Here, CP (Cost Price) for 121 fruits is 100 (since he bought 100 fruits). Thus:
\[ \text{SP} = 121 + 21\% \text{ of } 121 \]
First, calculate 21% of 121:
\[ 21\% \text{ of } 121 = \frac{21}{100} \times 121 = 25.41 \]
Now, add this to the effective quantity:
\[ \text{SP} = 121 + 25.41 = 146.41 \]

4. **Calculating the Gain**:
The gain can be calculated by subtracting the original cost price (CP) from the selling price (SP):
\[ \text{Gain} = \text{SP} - \text{CP} = 146.41 - 100 = 46.41 \]

5. **Calculating the Gain Percentage**:
The gain percentage is calculated as:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left(\frac{46.41}{100}\right) \times 100 = 46.41\% \]

### Final Answer:
The total gain percentage of the shopkeeper is **46.41%**.