From a can of super quality oil containing 96 litres, 12 litres are drawn out, and the can is filled up with interior quality of oil. The process is repeated thrice,finally what shall the number of litres of super oil left in the can?

Answer

To solve the problem step by step, we will use the concept of successive dilution.

### Step 1: Initial Setup
We start with 96 liters of super quality oil.

### Step 2: First Extraction and Replacement
1. We draw out 12 liters of super quality oil.
2. The amount of super quality oil left after the first extraction:
\[ \text{Super oil left} = 96 - 12 = 84 \text{ liters} \]
3. We then add 12 liters of inferior quality oil back into the can, so the total volume remains 96 liters.

### Step 3: Calculate the Ratio of Super Quality Oil
The ratio of super quality oil after the first replacement is:
\[ \text{Fraction of super oil} = \frac{84}{96} = \frac{7}{8} \]

### Step 4: Second Extraction and Replacement
1. We again draw out 12 liters of the mixture, which now contains both super quality and inferior quality oil.
2. The amount of super quality oil drawn out:
\[ \text{Super oil drawn out} = 12 \times \frac{7}{8} = 10.5 \text{ liters} \]
3. The super quality oil left after the second extraction:
\[ \text{Super oil left} = 84 - 10.5 = 73.5 \text{ liters} \]
4. We add 12 liters of inferior quality oil back, keeping the total at 96 liters.

### Step 5: Calculate the Ratio of Super Quality Oil Again
The new fraction of super quality oil after the second replacement is:
\[ \text{Fraction of super oil} = \frac{73.5}{96} \]

### Step 6: Third Extraction and Replacement
1. We draw out 12 liters of the mixture again.
2. The amount of super quality oil drawn out:
\[ \text{Super oil drawn out} = 12 \times \frac{73.5}{96} = 9.1875 \text{ liters} \]
3. The super quality oil left after the third extraction:
\[ \text{Super oil left} = 73.5 - 9.1875 = 64.3125 \text{ liters} \]
4. We add 12 liters of inferior quality oil back, keeping the total at 96 liters.

### Step 7: Final Amount of Super Quality Oil
After three extractions and replacements, the final amount of super quality oil left in the can is approximately:
\[ \text{Final super quality oil} \approx 64.3125 \text{ liters} \]

### Summary
The final amount of super quality oil left in the can after three cycles of extraction and replacement is approximately **64.31 liters**.

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