# Three containers are full of a mixture of alcohol and water in the ratio of 2 ∶ 1, 5 ∶ 1, and 3 ∶ 2 respectively. If the capacities of three container

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Three containers are full of a mixture of alcohol and water in the ratio of 2 ∶ 1, 5 ∶ 1, and 3 ∶ 2 respectively. If the capacities of three containers are in the ratio 3 ∶ 4 ∶ 3, then find the ratio of alcohol and water. If the mixture of all three containers is mixed together.
1. 112 ∶ 35
2. 110 ∶ 43
3. 107 ∶ 43
4. 103 ∶ 53
5.

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Correct Answer - Option 3 : 107 ∶ 43

Given:

Capacities ratio of three containers = 3 ∶ 4 ∶ 3

The ratio of alcohol to water in the first container = 2 ∶ 1

The ratio of alcohol to water in the second container = 5 ∶ 1

The ratio of alcohol to water in the third container = 3 ∶ 2

Calculation:

First, we have to make the sum of ratios equal

⇒ The ratio of alcohol to water in the first container = 2/1 = (2 × 10)/(1 × 10) = 20/10

⇒ The ratio of alcohol to water in the second container = 5/1 = (5 × 5)/(1 × 5) = 25/5

⇒ The ratio of alcohol to water in the third container = 3/2 = (3 × 6)/(2 × 6) = 18/12

Now, they are mixed in the ratio 3 ∶ 4 ∶ 3

Alcohol = (20 × 3) + (25 × 4) + (18 × 3)

⇒ 214

Water = (10 × 3) + (5 × 4) + (12 × 3)

⇒ 86

Ratio of alcohol to water = 214 ∶ 86 = 107 ∶ 43

∴ The ratio of alcohol to water is 107 ∶ 43.