There are two containers A and B. In container A, the ratio of milk and water is 1:3 and in container B, the ratio of milk and water is m: n. If the mixture in the containers A and B are mixed in the ratio 2:3 to get 20 litres of a mixture having milk and water in the ratio 3:7, then what is the value of \frac{m}{n} ?

  1. A. \frac{1}{2} ✓
  2. B. \frac{2}{3}
  3. C. \frac{3}{4}
  4. D. \frac{4}{5}

Correct Answer: A. \frac{1}{2}

Explanation

The 20 L mixture is made of A and B in ratio 2:3, meaning 8 L from A and 12 L from B. In 8 L of A (1:3), milk = 2 L, water = 6 L. The final 20 L mixture has ratio 3:7, so milk = 6 L, water = 14 L. The contribution from B must be 6 - 2 = 4 L milk and 14 - 6 = 8 L water. Thus, the ratio m:n in B is 4:8 = 1:2, so \frac{m}{n} = \frac{1}{2}.

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