`25%` of a solution containing ` 20%` petrol, `50%` diesel and ` 30% `kerosene was replaced with kerosene. Now, 2/3 of the solution obtained in the previous step was replaced with petrol. What is the percentage of diesel in this new solution ?

Answer

To solve the problem step by step, we will follow the operations described in the question and calculate the percentage of diesel in the final solution.

### Step 1: Initial Composition of the Solution
Let's assume we have a total solution of 100 liters. The composition of this solution is:
- Petrol: 20% of 100 liters = 20 liters
- Diesel: 50% of 100 liters = 50 liters
- Kerosene: 30% of 100 liters = 30 liters

### Step 2: Removing 25% of the Solution
We need to replace 25% of the solution with kerosene.
- 25% of 100 liters = 25 liters

After removing 25 liters, the remaining solution is:
- Remaining solution = 100 liters - 25 liters = 75 liters

### Step 3: Composition After Removal
Now we need to determine how much diesel is left after removing 25 liters of the solution. Since the original solution had 50 liters of diesel in 100 liters, the proportion of diesel in the solution is 50 liters out of 100 liters, or 50%.

The amount of diesel removed when we take out 25 liters of the solution:
- Diesel removed = 25 liters * (50/100) = 12.5 liters

Now, the remaining amount of diesel is:
- Remaining diesel = 50 liters - 12.5 liters = 37.5 liters

### Step 4: Adding Kerosene
After removing 25 liters of the solution, we replace it with 25 liters of kerosene. The new composition of the solution is:
- Petrol: 20 liters (unchanged)
- Diesel: 37.5 liters (after removal)
- Kerosene: 30 liters + 25 liters = 55 liters

### Step 5: New Total Volume of Solution
The total volume of the new solution remains 100 liters (75 liters remaining + 25 liters of kerosene added).

### Step 6: Replacing 2/3 of the New Solution with Petrol
Now we replace 2/3 of the new solution with petrol:
- 2/3 of 100 liters = 66.67 liters

The remaining solution after this operation is:
- Remaining solution = 100 liters - 66.67 liters = 33.33 liters

### Step 7: Composition After Second Replacement
Now we need to find out how much diesel remains after removing 66.67 liters from the new solution. The proportion of diesel in the new solution is:
- Diesel proportion = 37.5 liters out of 100 liters.

The amount of diesel removed when we take out 66.67 liters of the solution:
- Diesel removed = 66.67 liters * (37.5/100) = 25 liters (approximately)

Now, the remaining amount of diesel is:
- Remaining diesel = 37.5 liters - 25 liters = 12.5 liters

### Step 8: Final Composition of the Solution
After the second replacement, we have:
- Remaining solution = 33.33 liters
- Remaining diesel = 12.5 liters

### Step 9: Calculating the Percentage of Diesel
To find the percentage of diesel in the final solution:
- Percentage of diesel = (Remaining diesel / Total solution) * 100
- Percentage of diesel = (12.5 liters / 100 liters) * 100 = 12.5%

### Final Answer
The percentage of diesel in the new solution is **12.5%**.

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