Two vessels contain milk and water in the ratios 2 : 3 and 3 : 7. If the contents of the two vessels are mixed in the ratio 1 : 1 by volume, find the ratio of milk to water in the new mixture.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7 : 13
Take 1 litre from each vessel and add the milk fractions; the rest of the 2 litres is water.
Milk in 1 litre of the first \(=\frac{2}{5}\); of the second \(=\frac{3}{10}\)
Milk in 2 litres \(=\frac{2}{5}+\frac{3}{10}=\frac{7}{10}\); water \(=2-\frac{7}{10}=\frac{13}{10}\)
Milk : water \(=\frac{7}{10}:\frac{13}{10}=7:13\)
The new ratio is 7 : 13.
Why the other options are incorrect
Option (2) 4 : 3 — Incorrect. This compares the milk fractions of the two vessels, not milk with water in the mixture.
Option (3) 1 : 2 — Incorrect. This adds the ratio terms, 5 : 10; the two mixtures have different totals (5 and 10 parts), so the fractions must be added instead.
Option (4) 13 : 7 — Incorrect. This is water : milk, the ratio the wrong way round.