The cost price of 24 apples is same as the selling price of 18 apples. The percentage of gain is

Options

A. `12(1)/(2)%`
B. `14(2)/(3)%`
C. `18(2)/(3)%`
D. `33(1)/(3)%`

Answer

To solve the problem, we need to find the percentage of gain based on the given information. Let's break it down step by step.

### Step 1: Define Variables
Let the cost price of 1 apple be \( x \).

### Step 2: Calculate Cost Price of 24 Apples
The cost price of 24 apples is:
\[ \text{Cost Price of 24 Apples} = 24 \times x = 24x \]

### Step 3: Calculate Selling Price of 18 Apples
According to the problem, the cost price of 24 apples is the same as the selling price of 18 apples. Therefore:
\[ \text{Selling Price of 18 Apples} = 24x \]

### Step 4: Calculate Selling Price of 1 Apple
To find the selling price of 1 apple, we divide the selling price of 18 apples by 18:
\[ \text{Selling Price of 1 Apple} = \frac{24x}{18} = \frac{4x}{3} \]

### Step 5: Calculate Cost Price of 18 Apples
The cost price of 18 apples is:
\[ \text{Cost Price of 18 Apples} = 18 \times x = 18x \]

### Step 6: Calculate Gain
Gain is calculated as the selling price minus the cost price. Thus, the gain from selling 18 apples is:
\[ \text{Gain} = \text{Selling Price of 18 Apples} - \text{Cost Price of 18 Apples} \]
Substituting the values we have:
\[ \text{Gain} = 24x - 18x = 6x \]

### Step 7: Calculate Gain Percentage
The gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left( \frac{6x}{18x} \right) \times 100 = \left( \frac{6}{18} \right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
The percentage of gain is \( 33.33\% \).

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