Two vessels, A and B, have the same capacity and initially contain milk and water in the ratios of 5 : 1 and 3 : 1, respectively. First, 25% of the mixture from vessel A is removed and poured into vessel B. After thoroughly mixing the contents of vessel B, the same quantity is taken out and added back to vessel A. What is the ratio of milk to water in vessel A after this second transfer?1) 7 : 32) 77 : 233) 49 : 114) 81 : 19
Question
Two vessels, A and B, have the same capacity and initially contain milk and water in the ratios of 5 : 1 and 3 : 1, respectively. First, 25% of the mixture from vessel A is removed and poured into vessel B. After thoroughly mixing the contents of vessel B, the same quantity is taken out and added back to vessel A. What is the ratio of milk to water in vessel A after this second transfer?1) 7 : 32) 77 : 233) 49 : 114) 81 : 19
Solution
Let's assume the capacity of each vessel is 1 unit for simplicity.
In vessel A, the ratio of milk to water is 5:1. So, in 1 unit, there is 5/6 unit of milk and 1/6 unit of water.
In vessel B, the ratio of milk to water is 3:1. So, in 1 unit, there is 3/4 unit of milk and 1/4 unit of water.
First, 25% of the mixture from vessel A is removed and poured into vessel B. So, 0.25 unit is removed from A, which contains 0.25*(5/6) = 5/24 unit of milk and 0.25*(1/6) = 1/24 unit of water.
After this transfer, vessel A has (5/6 - 5/24) = 15/24 unit of milk and (1/6 - 1/24) = 3/24 unit of water.
Vessel B now has (3/4 + 5/24) = 23/24 unit of milk and (1/4 + 1/24) = 7/24 unit of water.
Then, 25% of the mixture from vessel B is removed and added back to vessel A. So, 0.25 unit is removed from B, which contains 0.25*(23/24) = 23/96 unit of milk and 0.25*(7/24) = 7/96 unit of water.
After this second transfer, vessel A has (15/24 + 23/96) = 77/96 unit of milk and (3/24 + 7/96) = 23/96 unit of water.
So, the ratio of milk to water in vessel A after this second transfer is 77:23.
Therefore, the answer is 2) 77 : 23.
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