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A large container has a 50 litre mixture of juice and water in the ratio 3 ∶ 2. To this, a 60 litre juice and water mixture is added, that has a juice to water ratio of 2 ∶ 1. After this, 11 litres of the solution is replaced with pure juice. What is the ratio of water to juice in the final mixture?

A large container has a 50 litre mixture of juice and water in the ratio 3 ∶ 2. To this, a 60 litre juice and water mixture is added, that has a juice to water ratio of 2 ∶ 1. After this, 11 litres of the solution is replaced with pure juice. What is the ratio of water to juice in the final mixture? Correct Answer 18 ∶ 37

Given:

Mixture of juice and water = 50 litre

The ratio of juice and water = 3 : 2

A 60 litre juice and water mixture is added, that has a juice to water ratio of 2 ∶ 1

After this, 11 litres of the solution is replaced with pure juice

Calculation:

The juice in the mixture = (3/5 × 50) = 30 litre

The water in the mixture = (2/5 × 50) = 20 litre

Now,

A 60 litre juice and water mixture is added, that has a juice to water ratio of 2 ∶ 1

The juice in the mixture = (2/3 × 60) = 40

The water in the mixture = (1/3 × 60) = 20

Now,

Total mixture of juice = (30 + 40) = 70 litre

Total mixture of water = (20 + 20) = 40 litre

The ratio of juice and water = (70 : 40)

⇒ 7 : 4

Now,

The ratio of juice = (70 – 7) = 63 litre

The ratio of water = (40 – 4) = 36 litre

Now,

11 litres of the solution is replaced with pure juice

⇒ (63 + 11) : 36

⇒ 74 : 36

⇒ 37 : 18

The ratio of water to juice in the final mixture = 18 : 37

∴ The required ratio is 18 : 37

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