A cloth merchant on selling 33 metre of cloth obtains a profit equal to the selling price of 11 metre of cloth. The profit percentage is :

Question

Accepted Answer

To determine the profit percentage, we need to analyze the information given in the question:

1. **Understanding the Problem:**
   - A cloth merchant sells 33 meters of cloth.
   - The profit obtained is equal to the selling price of 11 meters of cloth.

2. **Calculating the Selling Price and Profit:**
   - Let the selling price per meter of cloth be $ SP $.
   - Therefore, the selling price of 33 meters of cloth is $ 33 \times SP $.
   - The profit is equal to the selling price of 11 meters of cloth, which is $ 11 \times SP $.

3. **Calculating the Cost Price:**
   - The profit is the difference between the selling price and the cost price.
   - Let the cost price of 33 meters of cloth be $ CP $.
   - Therefore, the profit can also be expressed as $ 33 \times SP - CP $.

4. **Setting Up the Equation:**
   - Since the profit is equal to the selling price of 11 meters of cloth, we have:
     $$
     33 \times SP - CP = 11 \times SP
     $$
   - Simplifying this equation gives:
     $$
     CP = 33 \times SP - 11 \times SP = 22 \times SP
     $$

5. **Calculating the Profit Percentage:**
   - Profit percentage is calculated as:
     $$
     \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100
     $$
   - Substituting the values, we get:
     $$
     \text{Profit Percentage} = \left( \frac{11 \times SP}{22 \times SP} \right) \times 100 = \frac{11}{22} \times 100 = 50\%
     $$

6. **Conclusion:**
   - The profit percentage is 50%, which corresponds to Option 3.

**Explanation of Incorrect Options:**

- **Option 1 (11%):** This option is incorrect because the calculated profit percentage is significantly higher than 11%. The profit from selling 33 meters is much more substantial than what an 11% profit would imply.

- **Option 2 (22%):** This option is incorrect because the profit percentage calculation clearly shows a 50% profit, which is more than double 22%.

- **Option 4 (40%):** This option is incorrect because, although closer to the correct answer than Options 1 and 2, it still underestimates the actual profit percentage, which is 50%.

In conclusion, the correct profit percentage is 50%, making Option 3 the correct choice.