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Q86. A mixture contains milk and water in the ratio $4:1$. If 20% of the mixture is taken out and the same amount of milk and water is added to the mixture, then the difference between milk and water in the final mixture becomes 72 litres. Find the initial amount of the mixture.

1. 120 litre
2. 180 litre
3. 90 litre
4. 150 litre
5. None of these

Correct answer: 150 litre

Solution

Initially, if total mixture is $x$, milk = $\frac{4x}{5}$ and water = $\frac{x}{5}$, so the difference is $\frac{3x}{5}$. Removing 20% of the mixture and replacing it with equal amounts of milk and water reduces the difference to 80% of its original value, so final difference = $\frac{4}{5}\cdot \frac{3x}{5}=72$. Solving gives $x=150$ litres.

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