In a 180-litre mixture, there is 33.33% water and the rest is milk. If 54 litres of the mixture is removed and $x$ litres of milk is added, then the water content becomes 25%. Find the value of $x$.

Correct answer: 42

Solution

Initially, water is one-third of 180 litres, i.e. 60 litres, and milk is 120 litres. After removing 54 litres of the mixture, 18 litres water and 36 litres milk are removed, leaving 42 litres water; then adding $x$ litres milk makes the final volume $126+x$, and water is 25% of that. Solving gives $x=42$.

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