A sells vegetables at a profit of 35% and for weighing uses a weight which is 10% less than the article weight. What is total profit percentage?

Options

A. 50
B. 35
C. 45
D. 55

Answer

To find the total profit percentage when A sells vegetables at a profit of 35% and uses a weight that is 10% less than the actual weight, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the Cost Price (CP) of 1 kg of vegetables**:
- Let the cost price of 1 kg of vegetables be Rs 100.

**Hint**: Start by assuming a convenient value for the cost price to simplify calculations.

2. **Calculate the Effective Weight Used**:
- Since A uses a weight that is 10% less than the actual weight, the weight he uses is:
\[ \text{Effective Weight} = 1 \text{ kg} - (10\% \text{ of } 1 \text{ kg}) = 1 \text{ kg} - 0.1 \text{ kg} = 0.9 \text{ kg} \]

**Hint**: Remember that 10% less means you need to subtract 10% from the total weight.

3. **Calculate the Cost Price of the Effective Weight**:
- The cost price for the 0.9 kg of vegetables is:
\[ \text{CP of 0.9 kg} = 0.9 \text{ kg} \times \text{CP of 1 kg} = 0.9 \times 100 = Rs 90 \]

**Hint**: Use the proportion of the weight to find the cost price for the reduced weight.

4. **Calculate the Selling Price (SP) with Profit**:
- A sells the vegetables at a profit of 35%. Therefore, the selling price is:
\[ \text{SP} = \text{CP} + \text{Profit} = \text{CP} + (35\% \text{ of CP}) = 100 + (35\% \text{ of } 100) = 100 + 35 = Rs 135 \]

**Hint**: To find the selling price, add the profit percentage to the cost price.

5. **Calculate the Overall Profit**:
- The overall profit is calculated as:
\[ \text{Overall Profit} = \text{SP} - \text{CP of Effective Weight} = 135 - 90 = Rs 45 \]

**Hint**: Profit is the difference between selling price and cost price.

6. **Calculate the Total Profit Percentage**:
- The total profit percentage is given by:
\[ \text{Total Profit Percentage} = \left(\frac{\text{Overall Profit}}{\text{CP of Effective Weight}}\right) \times 100 = \left(\frac{45}{90}\right) \times 100 = 50\% \]

**Hint**: To find the percentage, divide the profit by the cost price and multiply by 100.

### Final Result:
The total profit percentage is **50%**.