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Three vessels of equal capacity are filled with a solution of alcohol and water. The ratio of alcohol and water in the first vessel is 2 ∶ 3, in the second vessel is 3 ∶ 4 , and in the third vessel is 4 ∶ 5. The solution of these 3 vessels is mixed into a bigger vessel. What is the ratio of alcohol to water in the bigger vessel?

Three vessels of equal capacity are filled with a solution of alcohol and water. The ratio of alcohol and water in the first vessel is 2 ∶ 3, in the second vessel is 3 ∶ 4 , and in the third vessel is 4 ∶ 5. The solution of these 3 vessels is mixed into a bigger vessel. What is the ratio of alcohol to water in the bigger vessel? Correct Answer 401 : 544

Given:

Ratio of alcohol to water in 1st, 2nd, and 3rd vessel = (2 ∶ 3), (3 ∶ 4), (4 ∶ 5) respectively

Concept:  

Equivalent amount to be taken from each vessel = LCM of the total (sum) ratio of alcohol and water in a vessel = LCM (5, 7 ,9) = 315

Calculation:

Let 315 unit of each is taken.

Alcohol : water ratio in each
1st vessel = 126 ∶  189
2nd vessel = 135 ∶  180
3rd vessel = 140 ∶  175
∴ Required ratio =  (126 + 135 + 140) ∶  (189 + 180 + 175) = 401 ∶  544

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