A man sells rice at 10% profit and uses weight 30% less than the actual measure. His gain per cent is

Options

A. `57(2)/(8)%`
B. `57(1)/(7)%`
C. `57(2)/(5)%`
D. `57(3)/(7)%`

Answer

To solve the problem step by step, we will analyze the situation of the man selling rice, taking into account both the profit percentage and the reduction in weight.

### Step 1: Understand the Given Data
- The man sells rice at a profit of 10%.
- He uses a weight that is 30% less than the actual measure.

### Step 2: Assume a Base Value
Let's assume the cost price (CP) of 1000 grams of rice is ₹1000.

### Step 3: Calculate Selling Price (SP)
Since he sells at a profit of 10%, we can calculate the selling price (SP) as follows:
\[ SP = CP + (10\% \text{ of } CP) = CP \times \left(1 + \frac{10}{100}\right) = 1000 \times \frac{110}{100} = 1100 \text{ rupees} \]

### Step 4: Calculate the Actual Weight Sold
Since he uses a weight that is 30% less, the actual weight sold is:
\[ \text{Actual weight sold} = 1000 \text{ grams} - (30\% \text{ of } 1000 \text{ grams}) = 1000 \times \left(1 - \frac{30}{100}\right) = 1000 \times \frac{70}{100} = 700 \text{ grams} \]

### Step 5: Calculate the Cost Price of the Actual Weight Sold
The cost price (CP) for 700 grams of rice can be calculated as:
\[ CP \text{ of } 700 \text{ grams} = \frac{700}{1000} \times 1000 = 700 \text{ rupees} \]

### Step 6: Calculate the Profit
Now, we can find the profit made by the man:
\[ \text{Profit} = SP - CP = 1100 - 700 = 400 \text{ rupees} \]

### Step 7: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP of actual weight sold}}\right) \times 100 = \left(\frac{400}{700}\right) \times 100 \]
\[ = \frac{40000}{700} \approx 57.14\% \]

### Final Answer
The gain percentage is approximately **57.14%**.

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