Discussion
A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water the ratio becomes 5 : 2. How much milk is in the mixture?
Answer: A
Correct answer: 25 litres
Let the milk be \( 5x \) and the water \( x \). The milk is unchanged by adding water, which is what makes the problem tractable. After adding 5 litres the water becomes \( x + 5 \), and \[ \frac{5x}{x + 5} = \frac{5}{2} \;\Rightarrow\; 10x = 5x + 25 \;\Rightarrow\; x = 5. \] The milk is therefore \( 5x = 25 \) litres. Checking: 25 litres of milk and 5 of water is 5 : 1; adding 5 litres of water gives 25 and 10, which is 5 : 2. A shortcut is available and worth knowing. Since the milk is constant, write both ratios with the same first term - here both are already 5 - and the water has gone from 1 part to 2 parts, an increase of 1 part. That 1 part equals the 5 litres added, so each part is 5 litres and the milk is 25.
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