The water and milk in two vessels are in the ratio 1:1 and 3:8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4:7?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2:3
The fraction of water in each mixture is:
\( \displaystyle \text{Vessel 1: } \frac{1}{1 + 1} = \frac{1}{2} \)
\( \displaystyle \text{Vessel 2: } \frac{3}{3 + 8} = \frac{3}{11} \)
\( \displaystyle \text{Required: } \frac{4}{4 + 7} = \frac{4}{11} \)
Let the two mixtures be taken in the ratio x : y. The water in the new mixture is the water from both vessels:
\( \displaystyle \frac{1}{2}x + \frac{3}{11}y = \frac{4}{11}(x + y) \)
Multiplying by 22:
\(11x + 6y = 8x + 8y\)
\(3x = 2y\)
\(x : y = 2 : 3\)