A vegetable seller sells his vegetables at 20% profit. At the same time he uses false weights, which is 10% less than the actual weight. What will be his total gain percentage ?

Options

A. 25
B. 30
C. 33.33
D. `18 7/9 %`

Answer

To find the total gain percentage of the vegetable seller who sells his vegetables at a 20% profit while using false weights that are 10% less than the actual weight, we can follow these steps:

### Step 1: Understand the Selling Price and Cost Price
Let’s assume the cost price (CP) of the vegetables is ₹100.

### Step 2: Calculate the Selling Price (SP)
The seller sells the vegetables at a 20% profit. Therefore, the selling price can be calculated as:
\[ SP = CP + (20\% \text{ of } CP) = 100 + (20/100 \times 100) = 100 + 20 = ₹120 \]

### Step 3: Calculate the Actual Weight Sold
Since the seller uses false weights that are 10% less than the actual weight, if he is supposed to sell 1 kg of vegetables, he actually sells:
\[ \text{Actual weight sold} = 1 \text{ kg} - (10\% \text{ of } 1 \text{ kg}) = 1 - 0.1 = 0.9 \text{ kg} \]

### Step 4: Calculate the Effective Cost Price for the Weight Sold
The cost price for 0.9 kg of vegetables can be calculated as:
\[ \text{Effective CP for 0.9 kg} = \left(\frac{CP}{1 \text{ kg}}\right) \times 0.9 = \frac{100}{1} \times 0.9 = ₹90 \]

### Step 5: Calculate the Gain
Now, we can calculate the gain made by the seller:
\[ \text{Gain} = SP - \text{Effective CP} = 120 - 90 = ₹30 \]

### Step 6: Calculate the Total Gain Percentage
The total gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{Effective CP}}\right) \times 100 = \left(\frac{30}{90}\right) \times 100 = \frac{1}{3} \times 100 \approx 33.33\% \]

### Final Answer
The total gain percentage of the vegetable seller is approximately **33.33%**.

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