Vessel A contains milk and water in the ratio 4 : 5. Vessel B contains milk and water in the ratio 2 : 1. If x litres mixture of A is mixed with y litres mixture of B, then the ratio of milk to water in the mixture becomes 8 : 5. Find the ratio of x : y.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 3 : 10.
Let x liters of A and y liters of B are mixed.
The amount of milk in the mixture = (4/9)x + (2/3)y
The amount of water in the mixture is (5/9)x + (1/3)y
So, [(4/9)x + (2/3)y]/[(5/9)x + (1/3)y] = 8/5
⇒ (20/9)x + (10/3)y = (40/9)x + (8/3)y
⇒ 20x + 30y = 40x + 24y
⇒ 6y = 20x
⇒ x/y = 3/10
Therefore, the required ratio is 3 : 10.