By selling 33 meters of cloth, A gets gain equal to selling price of 11 meters. Gain in percentage is equal to :

Question

Accepted Answer

To determine the gain percentage when selling 33 meters of cloth, where the gain is equal to the selling price of 11 meters, we need to follow these steps:

1. **Understanding the Problem:**
   - Let the cost price (CP) of 1 meter of cloth be $ x $.
   - Therefore, the cost price of 33 meters of cloth is $ 33x $.

2. **Selling Price and Gain:**
   - The gain is equal to the selling price of 11 meters of cloth.
   - Let the selling price (SP) of 1 meter of cloth be $ y $.
   - Therefore, the selling price of 33 meters of cloth is $ 33y $.
   - The gain is given as the selling price of 11 meters, which is $ 11y $.

3. **Calculating Gain:**
   - Gain = Selling Price - Cost Price
   - From the problem, Gain = $ 11y $.
   - Therefore, $ 33y - 33x = 11y $.

4. **Solving for Cost Price:**
   - Simplifying the equation: $ 33y - 11y = 33x $
   - $ 22y = 33x $
   - Dividing both sides by 11: $ 2y = 3x $
   - Therefore, $ y = \frac{3}{2}x $.

5. **Calculating Gain Percentage:**
   - Gain = $ 11y = 11 \times \frac{3}{2}x = \frac{33}{2}x $.
   - Gain Percentage = $\left(\frac{\text{Gain}}{\text{Cost Price}}\right) \times 100$
   - Gain Percentage = $\left(\frac{\frac{33}{2}x}{33x}\right) \times 100$
   - Gain Percentage = $\left(\frac{1}{2}\right) \times 100 = 50\%$.

Thus, the gain percentage is 50%, which corresponds to Option 3.

**Explanation for Incorrect Options:**

1. **Option 1 (25%):**
   - A 25% gain would imply that the gain is one-fourth of the cost price, which does not match the calculated gain of 50%.

2. **Option 2 (33$\frac{1}{3}$%):**
   - A 33$\frac{1}{3}$% gain would imply that the gain is one-third of the cost price, which is not consistent with the calculated gain of 50%.

3. **Option 4 (75%):**
   - A 75% gain would imply that the gain is three-fourths of the cost price, which exceeds the calculated gain of 50%.

Therefore, the correct answer is Option 3, which is 50%.