From a tank of petrol, which contains 200 litres of petrol, the seller replaces each time with kerosene when he sells 40 litres of petrol(or its mixture). Everything he sells out only 40 litres of petrol(pure or impure). After replacing the petrol with kerosene 4th time, the total amount of kerosene in the mixture is :

Options

A. 81.92 l
B. 96 l
C. 118.08 l
D. none of these

Explanation

To solve the problem, we need to calculate the amount of kerosene in the mixture after the seller has replaced petrol with kerosene four times, each time selling 40 liters of the mixture.

### Step-by-Step Solution:

1. **Initial Setup**:
- The tank initially contains 200 liters of petrol.
- The seller sells 40 liters of this mixture (petrol + kerosene) four times.

2. **Understanding the Mixture**:
- After each sale, the seller replaces the 40 liters sold with kerosene.
- We need to calculate the amount of petrol remaining after each sale and the corresponding increase in kerosene.

3. **First Sale**:
- Initial petrol = 200 liters, kerosene = 0 liters.
- When 40 liters are sold, the fraction of petrol sold = 40/200 = 0.2.
- Amount of petrol left = 200 - 40 = 160 liters.
- Kerosene added = 40 liters.
- Total mixture now = 160 liters petrol + 40 liters kerosene.

4. **Second Sale**:
- Total mixture = 200 liters (160 liters petrol + 40 liters kerosene).
- When 40 liters are sold, the fraction of petrol = 160/200 = 0.8.
- Amount of petrol sold = 0.8 * 40 = 32 liters.
- Amount of kerosene sold = 0.2 * 40 = 8 liters.
- Petrol remaining = 160 - 32 = 128 liters.
- Kerosene now = 40 - 8 + 40 = 72 liters.

5. **Third Sale**:
- Total mixture = 200 liters (128 liters petrol + 72 liters kerosene).
- When 40 liters are sold, the fraction of petrol = 128/200 = 0.64.
- Amount of petrol sold = 0.64 * 40 = 25.6 liters.
- Amount of kerosene sold = 0.36 * 40 = 14.4 liters.
- Petrol remaining = 128 - 25.6 = 102.4 liters.
- Kerosene now = 72 - 14.4 + 40 = 97.6 liters.

6. **Fourth Sale**:
- Total mixture = 200 liters (102.4 liters petrol + 97.6 liters kerosene).
- When 40 liters are sold, the fraction of petrol = 102.4/200 = 0.512.
- Amount of petrol sold = 0.512 * 40 = 20.48 liters.
- Amount of kerosene sold = 0.488 * 40 = 19.52 liters.
- Petrol remaining = 102.4 - 20.48 = 81.92 liters.
- Kerosene now = 97.6 - 19.52 + 40 = 118.08 liters.

### Final Result:
After the fourth sale, the total amount of kerosene in the mixture is **118.08 liters**.