By selling 50 metres of cloth, a person gains the cost price of 20 metres of cloth. What is his gain percent?

Options

A. 40
B. 25
C. 20
D. 10

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the Cost Price (CP)
Let's assume the cost price of 1 meter of cloth is \( X \).

### Step 2: Calculate the Cost Price of 50 Meters
The cost price of 50 meters of cloth will be:
\[ \text{CP of 50 meters} = 50 \times X = 50X \]

### Step 3: Calculate the Gain
The problem states that by selling 50 meters of cloth, the person gains the cost price of 20 meters of cloth. Therefore, the gain is:
\[ \text{Gain} = \text{CP of 20 meters} = 20 \times X = 20X \]

### Step 4: Calculate the Selling Price (SP)
The selling price of 50 meters of cloth can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Substituting the values we found:
\[ \text{SP} = 50X + 20X = 70X \]

### Step 5: Calculate the Profit
Profit can be calculated as:
\[ \text{Profit} = \text{SP} - \text{CP} = 70X - 50X = 20X \]

### Step 6: Calculate the Gain Percent
The gain percent can be calculated using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percent} = \left( \frac{20X}{50X} \right) \times 100 \]
Simplifying this:
\[ \text{Gain Percent} = \left( \frac{20}{50} \right) \times 100 = 0.4 \times 100 = 40\% \]

### Final Answer
The gain percent is **40%**.

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