A fruit seller bought 600 mangoes at 6 for Rs. 5 and sold at 5 for Rs. 6. Find the profit or loss percentage :

Question

Accepted Answer

To determine the profit or loss percentage, we need to calculate the cost price (CP) and the selling price (SP) of the mangoes and then find the percentage difference.

1. **Cost Price Calculation:**
   - The fruit seller bought 600 mangoes at a rate of 6 mangoes for Rs. 5.
   - Therefore, the cost price for 600 mangoes is calculated as follows:
     $$
     \text{CP of 600 mangoes} = \left(\frac{600}{6}\right) \times 5 = 100 \times 5 = 500 \text{ Rs.}
     $$

2. **Selling Price Calculation:**
   - The fruit seller sold the mangoes at a rate of 5 mangoes for Rs. 6.
   - Therefore, the selling price for 600 mangoes is calculated as follows:
     $$
     \text{SP of 600 mangoes} = \left(\frac{600}{5}\right) \times 6 = 120 \times 6 = 720 \text{ Rs.}
     $$

3. **Profit Calculation:**
   - Profit is calculated as the difference between the selling price and the cost price:
     $$
     \text{Profit} = \text{SP} - \text{CP} = 720 - 500 = 220 \text{ Rs.}
     $$

4. **Profit Percentage Calculation:**
   - The profit percentage is calculated using the formula:
     $$
     \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{220}{500}\right) \times 100 = 44\%
     $$

Therefore, the profit percentage is 44%, which confirms that Option 1 is correct.

**Explanation for Incorrect Options:**

- **Option 2 (Loss 44%):** This option is incorrect because the calculations clearly show a profit, not a loss. The selling price is higher than the cost price, resulting in a profit.

- **Option 3 (Profit 22%):** This option is incorrect because the profit percentage calculated is 44%, not 22%. The calculations show a higher profit margin than 22%.

- **Option 4 (Loss 22%):** This option is incorrect because there is no loss in this transaction. The calculations indicate a profit, not a loss, and the percentage is also not 22%.

In conclusion, the correct answer is Option 1, which indicates a profit of 44%.