A shopkeeper cheats to the extent of `10%` while buying and selling fruits , by using tampere weights. His total gain, in percentage , is

Options

A. 21
B. 24
C. 22
D. 23

Answer

To find the total gain percentage of the shopkeeper who cheats by 10% while buying and selling fruits, we can follow these steps:

### Step 1: Understand the cheating percentage
The shopkeeper cheats by 10% while buying and selling. This means that when he buys fruits, he gets 10% more than what he pays for, and when he sells, he sells 10% less than what he claims.

### Step 2: Calculate the effective cost price (CP)
Assume the actual cost price (CP) of the fruits is 100 units (this can be in any currency). Since he cheats by 10% while buying, he effectively receives 10% more fruits. Therefore, the effective cost price becomes:
\[ \text{Effective CP} = 100 - 10\% \text{ of } 100 = 100 - 10 = 90 \]

### Step 3: Calculate the effective selling price (SP)
Now, when selling, he also cheats by 10%. If he claims to sell 100 units, he actually sells only 90 units. Therefore, the effective selling price becomes:
\[ \text{Effective SP} = 100 + 10\% \text{ of } 100 = 100 + 10 = 110 \]

### Step 4: Calculate the profit
Now we can calculate the profit made by the shopkeeper:
\[ \text{Profit} = \text{Effective SP} - \text{Effective CP} = 110 - 90 = 20 \]

### Step 5: Calculate the profit percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Effective CP}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Profit Percentage} = \left( \frac{20}{90} \right) \times 100 \approx 22.22\% \]

### Step 6: Round the profit percentage
Since the options provided are whole numbers, we can round 22.22% to the nearest whole number, which is 22%.

### Conclusion
The total gain percentage of the shopkeeper is approximately **22%**.

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