A trader mixes `25%` kerosene to his petrol and then he sells the whole mixture at the price of petrol. If the cost price of kerosene be `50%` of the cost price of petrol/what is the net profit percentage?

Options

A. `11(1)/9%`
B. `12(1)/9%
C. `9(1)/11%`
D. `20%`

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Define Variables**:
Let the cost price of petrol be \( P \). According to the problem, the cost price of kerosene is \( 50\% \) of the cost price of petrol. Therefore, the cost price of kerosene, \( K \), can be expressed as:
\[ K = 0.5P \]

2. **Determine Quantities**:
The trader mixes \( 25\% \) kerosene with petrol. If we assume we have \( 1 \) liter of petrol, then the amount of kerosene mixed will be:
\[ \text{Amount of kerosene} = 0.25 \times 1 = 0.25 \text{ liters} \]
Thus, the total quantity of the mixture is:
\[ \text{Total mixture} = 1 + 0.25 = 1.25 \text{ liters} \]

3. **Calculate Total Cost**:
The cost of the petrol is:
\[ \text{Cost of petrol} = P \]
The cost of the kerosene is:
\[ \text{Cost of kerosene} = 0.25 \times K = 0.25 \times 0.5P = 0.125P \]
Therefore, the total cost of the mixture is:
\[ \text{Total cost} = P + 0.125P = 1.125P \]

4. **Calculate Selling Price**:
The trader sells the entire mixture at the price of petrol. Since the selling price of petrol is \( P \) per liter, the selling price of the entire mixture (1.25 liters) is:
\[ \text{Selling Price} = 1.25 \times P = 1.25P \]

5. **Calculate Profit**:
The profit can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Total Cost} = 1.25P - 1.125P = 0.125P \]

6. **Calculate Profit Percentage**:
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total Cost}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{0.125P}{1.125P} \right) \times 100 = \left( \frac{0.125}{1.125} \right) \times 100 \]
Simplifying this gives:
\[ \text{Profit Percentage} = \frac{125}{112.5} = 11.11\% \]

### Final Answer:
The net profit percentage is approximately \( 11.11\% \).