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). Everytime 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

Answer

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

### Step-by-step Solution:

1. **Initial Setup:**
- The tank initially contains 200 litres of petrol.
- Each time 40 litres is sold, it is replaced with 40 litres of kerosene.

2. **First Replacement:**
- When the seller sells 40 litres of petrol, he removes 40 litres of petrol from the tank.
- Remaining petrol = 200 - 40 = 160 litres.
- After adding 40 litres of kerosene, the total mixture = 160 litres of petrol + 40 litres of kerosene = 200 litres.

3. **Second Replacement:**
- Now, the mixture has 160 litres of petrol and 40 litres of kerosene.
- When 40 litres of this mixture is sold, we need to find the ratio of petrol to kerosene in the mixture:
- Petrol in the mixture = 160 litres
- Kerosene in the mixture = 40 litres
- Total mixture = 200 litres
- Petrol fraction = 160/200 = 0.8
- Kerosene fraction = 40/200 = 0.2

- Amount of petrol sold = 40 litres * 0.8 = 32 litres
- Amount of kerosene sold = 40 litres * 0.2 = 8 litres

- Remaining petrol = 160 - 32 = 128 litres
- Remaining kerosene = 40 - 8 = 32 litres
- After adding 40 litres of kerosene, the new total mixture = 128 litres of petrol + 32 litres of kerosene + 40 litres of kerosene = 200 litres.

4. **Third Replacement:**
- Now, the mixture has 128 litres of petrol and 72 litres of kerosene.
- Selling 40 litres of this mixture:
- Petrol fraction = 128/200 = 0.64
- Kerosene fraction = 72/200 = 0.36

- Amount of petrol sold = 40 litres * 0.64 = 25.6 litres
- Amount of kerosene sold = 40 litres * 0.36 = 14.4 litres

- Remaining petrol = 128 - 25.6 = 102.4 litres
- Remaining kerosene = 72 - 14.4 = 57.6 litres
- After adding 40 litres of kerosene, the new total mixture = 102.4 litres of petrol + 57.6 litres of kerosene + 40 litres of kerosene = 200 litres.

5. **Fourth Replacement:**
- Now, the mixture has 102.4 litres of petrol and 97.6 litres of kerosene.
- Selling 40 litres of this mixture:
- Petrol fraction = 102.4/200 = 0.512
- Kerosene fraction = 97.6/200 = 0.488

- Amount of petrol sold = 40 litres * 0.512 = 20.48 litres
- Amount of kerosene sold = 40 litres * 0.488 = 19.52 litres

- Remaining petrol = 102.4 - 20.48 = 81.92 litres
- Remaining kerosene = 97.6 - 19.52 = 78.08 litres
- After adding 40 litres of kerosene, the new total mixture = 81.92 litres of petrol + 78.08 litres of kerosene + 40 litres of kerosene = 200 litres.

6. **Final Calculation of Kerosene:**
- After the fourth replacement, the total amount of kerosene in the mixture = 78.08 + 40 = 118.08 litres.

### Final Answer:
The total amount of kerosene in the mixture after the fourth replacement is **118.08 litres**.