If the cost price of 15 apples is same as the selling price of 20 apples. What is the gain or loss per cent?

Answer

To solve the problem step by step, we will first define the variables and then calculate the cost price and selling price of the apples.

### Step 1: Define the Cost Price (CP) and Selling Price (SP)
Let the cost price of 1 apple be \( CP \).
Then, the cost price of 15 apples is \( 15 \times CP = 15CP \).

Let the selling price of 1 apple be \( SP \).
Then, the selling price of 20 apples is \( 20 \times SP = 20SP \).

### Step 2: Set up the equation
According to the problem, the cost price of 15 apples is equal to the selling price of 20 apples:
\[ 15CP = 20SP \]

### Step 3: Express Selling Price in terms of Cost Price
From the equation \( 15CP = 20SP \), we can express the selling price per apple in terms of the cost price:
\[ SP = \frac{15CP}{20} \]
\[ SP = \frac{3CP}{4} \]

### Step 4: Calculate Gain or Loss
Now, we can find the gain or loss per apple:
- Gain or Loss = Selling Price - Cost Price
- Gain or Loss = \( SP - CP \)
Substituting the value of \( SP \):
\[ Gain/Loss = \frac{3CP}{4} - CP \]
\[ Gain/Loss = \frac{3CP}{4} - \frac{4CP}{4} \]
\[ Gain/Loss = -\frac{1CP}{4} \]

This indicates a loss of \( \frac{1CP}{4} \) per apple.

### Step 5: Calculate Loss Percentage
To find the loss percentage, we use the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{\frac{1CP}{4}}{CP} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{1}{4} \right) \times 100 \]
\[ \text{Loss Percentage} = 25\% \]

### Conclusion
Thus, the loss percentage is **25%**.

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