By selling 33 metres of cloth. a person gains the cost of 11 metres. Find his gain%.

Options

A. 33 `1/3` %
B. 33 `1/2` %
C. `35`%
D. 34 `1/3` %

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Cost Price
Let the cost price of 1 meter of cloth be \( x \).

### Step 2: Calculate the Cost Price for 11 meters and 33 meters
- The cost price of 11 meters of cloth is \( 11x \).
- The cost price of 33 meters of cloth is \( 33x \).

### Step 3: Define the Selling Price
Let the selling price of 1 meter of cloth be \( y \).
- Therefore, the selling price for 33 meters of cloth is \( 33y \).

### Step 4: Calculate the Gain
According to the problem, the gain is equal to the cost of 11 meters:
- Gain = Selling Price - Cost Price
- Gain = \( 33y - 33x \)

Since the gain is also equal to the cost of 11 meters:
- \( 33y - 33x = 11x \)

### Step 5: Rearrange the Equation
Rearranging the equation gives:
- \( 33y = 33x + 11x \)
- \( 33y = 44x \)

### Step 6: Simplify the Equation
Dividing both sides by 11:
- \( 3y = 4x \)
- This implies \( \frac{y}{x} = \frac{4}{3} \)

### Step 7: Calculate the Profit
The profit can be calculated as:
- Profit = Selling Price - Cost Price
- Profit = \( 33y - 33x = 33(y - x) \)

Substituting \( y \) from the ratio:
- \( y - x = \frac{4}{3}x - x = \frac{1}{3}x \)
- Therefore, Profit = \( 33 \times \frac{1}{3}x = 11x \)

### Step 8: Calculate the Gain Percentage
Gain Percentage is calculated as:
- Gain Percentage = \( \frac{\text{Profit}}{\text{Cost Price}} \times 100 \)
- Cost Price for 33 meters = \( 33x \)
- Gain Percentage = \( \frac{11x}{33x} \times 100 = \frac{11}{33} \times 100 = \frac{1}{3} \times 100 = 33.33\% \)

### Final Answer
The gain percentage is \( 33 \frac{1}{3}\% \).

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