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There are two vessels in which alcohol and water are in the ratio of 77 : 23 and 9 : 1 respectively. After mixing the two mixture in certain ratio a new mixture form having alcohol and water in the ratio of 4 : 1. Find in which ratio the two mixture mixed?

There are two vessels in which alcohol and water are in the ratio of 77 : 23 and 9 : 1 respectively. After mixing the two mixture in certain ratio a new mixture form having alcohol and water in the ratio of 4 : 1. Find in which ratio the two mixture mixed? Correct Answer 10 : 3

GIVEN:

Ratio of wine and water in two vessels = 77 : 23 and 9 : 1 respectively

New ratio of wine and water = 4 : 1

CALCULATION:

Let that from first vessel x litre is taken and from second vessel y litre is taken.

Total alcohol in the mixture = (77/100) × (x) + (9/10) × y

⇒ (4/5) × (x + y) = (77x + 90y)/100

⇒ (4x + 4y)/5 = (77x + 90y)/100

⇒ 400x + 400y = (385x + 450y)

⇒ 15x = 50y

∴ x/y = 10/3

Alternative method:

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