Discussion
A mixture of 45 litres has milk and water in the ratio 4 : 1. How much water must be added so that the ratio becomes 3 : 2?
Answer: C
Correct answer: 15 litres
The 45 litres contains \( 45 \times \frac{4}{5} = 36 \) litres of milk and 9 of water. The milk does not change. For a final ratio of 3 : 2 the water must be \( \frac{2}{3} \) of the milk, so it must become \[ \frac{2}{3} \times 36 = 24 \text{ litres}. \] The water to add is \[ 24 - 9 = 15 \text{ litres}. \] Checking: the vessel then holds 36 litres of milk and 24 of water, a total of 60 in the ratio 3 : 2. A quicker route uses parts. Expressing both ratios with the milk fixed - \( 4 : 1 \) becomes \( 12 : 3 \) and \( 3 : 2 \) becomes \( 12 : 8 \) - shows the water rising from 3 parts to 8, an increase of 5 parts. Since 12 parts of milk is 36 litres, one part is 3 litres, and 5 parts is 15.
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