If a mixture contains milk and water in the ratio of 4:1. If 20\% of the mixture is taken out and the same amount of milk and water are added into the mixture, then the difference between milk and water in the final mixture becomes 72 liters. Find the initial amount of mixture.

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Accepted Answer

**Solution:**

1. Let the total quantity of the mixture be $25y$ liters (since ratio is 4:1, total parts = 4 + 1 = 5, multiplied by 5 to avoid fractions).

2. Quantity of milk = $20y$ liters and quantity of water = $5y$ liters.

3. When 20\% of the mixture is taken out, the quantity taken out is $0.2 	imes 25y = 5y$ liters.

4. Milk taken out = 20\% of milk = $0.2 	imes 20y = 4y$ liters.

5. Water taken out = 20\% of water = $0.2 	imes 5y = 1y$ liters.

6. Remaining milk = $20y - 4y = 16y$ liters.

7. Remaining water = $5y - 1y = 4y$ liters.

8. Let the quantity of milk and water added be $x$ liters each.

9. After addition, milk = $16y + x$ liters, water = $4y + x$ liters.

10. According to the question, difference between milk and water after addition is 72 liters:

$$ (16y + x) - (4y + x) = 72 $$

Simplifies to:

$$ 12y = 72 $$

$$ y = 6 $$

11. Initial amount of mixture = $25y = 25 	imes 6 = 150$ liters.

**Answer:** 150 liter

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