Two containers A and B hold milk and water in the ratios 5 : 3 and 3 : 2 respectively. The two mixtures are mixed in the ratio 2 : 1 by volume. Find the ratio of milk to water in the new mixture.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 37 : 23
Take 2 litres of A and 1 litre of B and add the milk in each; the rest is water.
Milk in A \(=\frac{5}{8}\) of each litre; in B \(=\frac{3}{5}\)
Milk \(=2\times\frac{5}{8}+1\times\frac{3}{5}=\frac{37}{20}\); water \(=3-\frac{37}{20}=\frac{23}{20}\)
Milk : water \(=37:23\)
The new ratio is 37 : 23.
Why the other options are incorrect
Option (1) 73 : 47 — Incorrect. This takes 2 parts of the second mixture and 1 of the first, the wrong way round.
Option (2) 13 : 8 — Incorrect. This multiplies the ratio terms directly; the two mixtures have different totals, so the milk fractions must be used.
Option (4) 49 : 31 — Incorrect. This mixes the two in the ratio 1 : 1, not 2 : 1.