Two containers are taken such that capacity of first is one tenth of second. In both of them, 3 litres of milk and 7 litres of water is added. Now, from second container, 4 litres of the mixture is taken out and added to first container. The first container gets full after this process. With a mixture of milk and water, the remaining portion of second container is to be filled so that the final ratio of milk and water in second container becomes 2:3. What should be the ratio of milk and water in the added mixture?
Solution
Correct Answer: Option C
In containers, 3 litres of milk and 7 litres of water is added. Now, from second container, 4 litres of the mixture is taken out and added to first container. The first container gets full after this process.
⇒ Capacity of first container = (3 + 7 + 4) litres = 14 litres
⇒ Capacity of second container = 10 × 14 litres = 140 litres
Now, in second container, amount of mixture = (3 + 7 - 4) litres = 6 litres
Empty part of second container = (140 – 6) litres = 134 litres
Amount of milk is second container = (3/10) × 6 = 1.8 litres
Amount of water is second container = (7/10) × 6 = 4.2 litres
With a mixture of milk and water, the remaining portion of second container is to be filled so that the final ratio of milk and water in second container becomes 2:3.
Suppose the amounts of milk and water in added mixture is M:(134-M).
⇒ (1.8 + M)/(4.2 + 134 – M) = 2/3
⇒ 5.4 + 3M = 276.4 – 2M
⇒ 5M = 271
⇒ M = 54.2
∴ Ratio of milk and water in added mixture = 54.2/(134-54.2) = 54.2/79.8 = 271/399
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