Each question has four options(A), (B), (C) and (D) for answers. Select the right answer and write in English letters in the box against each question in the enclosed answer sheet.
By selling 100 oranges, a vendor gains the selling price of 20 oranges. His gain per cent is

Options

A. 20
B. 25
C. 30
D. 32

Answer

To find the gain percentage of the vendor who sells 100 oranges and gains the selling price of 20 oranges, we can follow these steps:

### Step 1: Understand the problem
The vendor sells 100 oranges and gains the selling price of 20 oranges. We need to find the gain percentage.

### Step 2: Define the terms
- Let the selling price (SP) of one orange be \( x \).
- Therefore, the selling price of 100 oranges = \( 100x \).
- The gain (profit) is equal to the selling price of 20 oranges, which is \( 20x \).

### Step 3: Calculate the cost price (CP)
The cost price (CP) of 100 oranges can be calculated using the formula:
\[ \text{Gain} = \text{SP} - \text{CP} \]
Since the gain is \( 20x \):
\[ 20x = 100x - \text{CP} \]
Rearranging this gives:
\[ \text{CP} = 100x - 20x = 80x \]

### Step 4: Calculate the profit
Profit is defined as:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values we have:
\[ \text{Profit} = 100x - 80x = 20x \]

### Step 5: Calculate the gain percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{20x}{80x} \right) \times 100 \]

### Step 6: Simplify the expression
The \( x \) in the numerator and denominator cancels out:
\[ \text{Gain Percentage} = \left( \frac{20}{80} \right) \times 100 \]
\[ = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Final Answer
The gain percentage of the vendor is **25%**.

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