A dishonest grocer sells rice at a profit of `10%` and also used weights which are `20%` less than the marked weight. The total gain earned by him will be

Options

A. `35%`
B. `37.5%`
C. `40%`
D. `30.5%`

Answer

To solve the problem, we need to calculate the total gain earned by the dishonest grocer who sells rice at a profit of 10% and uses weights that are 20% less than the marked weight.

### Step-by-Step Solution:

1. **Assume the Cost Price (CP)**:
Let's assume the cost price of 1 kg of rice is ₹100.

2. **Calculate the Selling Price (SP)**:
The grocer sells rice at a profit of 10%. Therefore, the selling price can be calculated as:
\[ SP = CP + (10\% \text{ of } CP) = 100 + (10\% \text{ of } 100) = 100 + 10 = ₹110 \]

3. **Determine the Actual Weight Sold**:
The grocer uses weights that are 20% less than the marked weight. Therefore, if the marked weight is 1 kg (1000 grams), the actual weight sold is:
\[ \text{Actual Weight} = 1000 \text{ grams} - (20\% \text{ of } 1000 \text{ grams}) = 1000 - 200 = 800 \text{ grams} \]

4. **Calculate the Cost Price of the Actual Weight**:
The cost price of 800 grams can be calculated as follows:
\[ \text{Cost Price of 800 grams} = \left(\frac{100 \text{ (CP of 1 kg)}}{1000 \text{ grams}}\right) \times 800 \text{ grams} = \frac{100}{1000} \times 800 = ₹80 \]

5. **Calculate the Profit**:
The profit earned by the grocer when selling 800 grams at ₹110 is:
\[ \text{Profit} = SP - CP = 110 - 80 = ₹30 \]

6. **Calculate the Profit Percentage**:
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}} \times 100\right) = \left(\frac{30}{80} \times 100\right) \]
Simplifying this gives:
\[ \text{Profit Percentage} = \frac{30 \times 100}{80} = \frac{3000}{80} = 37.5\% \]

### Final Answer:
The total gain earned by the dishonest grocer is **37.5%**.

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