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Three vessels whose capacities are in the ratio of 3: 2: 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5: 2, 4: 1 and 4: 1 respectively. Taking 1/3 of first, 1/2 of second and 1/7 of third mixtures, a new mixture kept in new vessel is prepared. The percentage of water in the new mixture is

Question

Three vessels whose capacities are in the ratio of 3: 2: 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5: 2, 4: 1 and 4: 1 respectively. Taking 1/3 of first, 1/2 of second and 1/7 of third mixtures, a new mixture kept in new vessel is prepared. The percentage of water in the new mixture is

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Solution

To solve this problem, we need to first understand the amount of milk and water in each vessel and then calculate the amount taken from each to form the new mixture.

  1. The capacities of the vessels are in the ratio 3:2:1. Let's assume the capacities to be 3x, 2x, and x respectively.

  2. The ratio of milk to water in the first vessel is 5:2. So, in a total of 3x, the amount of milk is 5/73x = 15x/7 and the amount of water is 2/73x = 6x/7.

  3. The ratio of milk to water in the second vessel is 4:1. So, in a total of 2x, the amount of milk is 4/52x = 8x/5 and the amount of water is 1/52x = 2x/5.

  4. The ratio of milk to water in the third vessel is also 4:1. So, in a total of x, the amount of milk is 4/5x = 4x/5 and the amount of water is 1/5x = x/5.

  5. Now, we take 1/3 from the first vessel, 1/2 from the second vessel, and 1/7 from the third vessel to form a new mixture. The amount of milk in the new mixture is 1/315x/7 + 1/28x/5 + 1/7*4x/5 = 5x/7 + 4x/5 + 4x/35 = 25x/35 + 28x/35 + 4x/35 = 57x/35.

  6. Similarly, the amount of water in the new mixture is 1/36x/7 + 1/22x/5 + 1/7*x/5 = 2x/7 + x/5 + x/35 = 10x/35 + 7x/35 + x/35 = 18x/35.

  7. The percentage of water in the new mixture is (18x/35) / (57x/35 + 18x/35) * 100 = 18 / 75 * 100 = 24%.

So, the percentage of water in the new mixture is 24%.

This problem has been solved

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