Discussion
Two vessels contain milk and water in the ratios 4 : 3 and 2 : 3. Equal quantities from each are mixed. What is the ratio of milk to water in the new mixture?
Answer: B
Correct answer: 17 : 18
Take equal quantities from each vessel - a convenient amount is the LCM of the ratio totals, 7 and 5, which is 35 litres from each. From the first vessel, 35 litres in the ratio 4 : 3 gives 20 of milk and 15 of water. From the second, 35 litres in the ratio 2 : 3 gives 14 of milk and 21 of water. Combining, \[ \text{milk} = 20 + 14 = 34, \qquad \text{water} = 15 + 21 = 36, \] so the ratio is \( 34 : 36 = \mathbf{17 : 18} \). Choosing the LCM as the common quantity is what keeps every figure a whole number; taking 1 litre from each would give fractions and the same answer more painfully. The check that costs nothing: the first vessel is richer in milk than the second, so the mixture must lie between \( 4/7 \approx 0.57 \) and \( 2/5 = 0.40 \) as a fraction of milk - and \( 17/35 \approx 0.49 \) does.
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