The cost price of 12 candles is equal to the selling price of 15 candles.Find the loss per cent

Answer

To solve the problem, we need to find the loss percentage when the cost price of 12 candles is equal to the selling price of 15 candles. Let's break it down step by step.

### Step 1: Define Variables
Let the cost price of one candle be \( CP \) and the selling price of one candle be \( SP \).

### Step 2: Write the Cost Price and Selling Price Equations
From the problem, we know:
- The cost price of 12 candles = \( 12 \times CP \)
- The selling price of 15 candles = \( 15 \times SP \)

According to the problem statement:
\[ 12 \times CP = 15 \times SP \]

### Step 3: Express Selling Price in terms of Cost Price
We can rearrange the equation to express \( SP \) in terms of \( CP \):
\[ SP = \frac{12}{15} \times CP \]
\[ SP = \frac{4}{5} \times CP \]

### Step 4: Calculate the Loss
Now, we can find the loss incurred on each candle:
Loss per candle = Cost Price - Selling Price
\[ \text{Loss} = CP - SP \]
Substituting the value of \( SP \):
\[ \text{Loss} = CP - \frac{4}{5} \times CP \]
\[ \text{Loss} = \frac{1}{5} \times CP \]

### Step 5: Calculate Loss Percentage
Loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]
Substituting the loss we calculated:
\[ \text{Loss Percentage} = \left( \frac{\frac{1}{5} \times CP}{CP} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{1}{5} \right) \times 100 \]
\[ \text{Loss Percentage} = 20\% \]

### Final Answer
The loss percentage is **20%**.

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