A vessel contains 240 liters of petrol. 20 liters of petrol taken out from it and completely replaced by kerosene and then again from the mixture 20 liters of mixture taken out and completely replaced by kerosene. Find the remaining quantity of petrol in the final mixture.

Options

A. 166.67 lit
B. 233.33 lit
C. 217.17 lt
D. 201.67 lit

Answer

To solve the problem step by step, we will follow the process of removing petrol and replacing it with kerosene.

### Step 1: Initial Setup
We have a vessel containing 240 liters of petrol.

### Step 2: First Removal
We remove 20 liters of petrol from the vessel.
- Remaining petrol = 240 liters - 20 liters = 220 liters of petrol.
- We replace the 20 liters taken out with 20 liters of kerosene.
- Now, the mixture contains 220 liters of petrol and 20 liters of kerosene.

### Step 3: Calculate the Fraction of Petrol
After the first removal and replacement, the total volume of the mixture is still 240 liters. The fraction of petrol in the mixture is:
- Fraction of petrol = Remaining petrol / Total mixture = 220 liters / 240 liters = 11/12.

### Step 4: Second Removal
Now, we take out 20 liters of this new mixture (which contains both petrol and kerosene).
- Amount of petrol in the 20 liters taken out = (11/12) * 20 liters = 18.33 liters (approximately).
- Amount of kerosene in the 20 liters taken out = (1/12) * 20 liters = 1.67 liters (approximately).

### Step 5: Update the Quantities
After removing 20 liters of the mixture, we have:
- Remaining petrol = 220 liters - 18.33 liters = 201.67 liters (approximately).
- Remaining kerosene = 20 liters - 1.67 liters = 18.33 liters (approximately).
- We then replace the 20 liters taken out with 20 liters of kerosene.
- New total of kerosene = 18.33 liters + 20 liters = 38.33 liters (approximately).

### Step 6: Final Mixture
Now, the final quantities in the vessel are:
- Petrol = 201.67 liters (approximately).
- Kerosene = 38.33 liters (approximately).

### Conclusion
The remaining quantity of petrol in the final mixture is approximately **201.67 liters**.

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