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A container is full of a mixture of alcohol and water. The ratio of alcohol to water in the mixture is 1 : 4. If some amount of mixture is taken out and it is filled with water then the ratio of alcohol to water becomes 1 : 9. If the size of a container is 10litre then how much water is added into the mixture?

A container is full of a mixture of alcohol and water. The ratio of alcohol to water in the mixture is 1 : 4. If some amount of mixture is taken out and it is filled with water then the ratio of alcohol to water becomes 1 : 9. If the size of a container is 10litre then how much water is added into the mixture? Correct Answer 5 litre

Let the amount of water added to the mixture be M litre.

Total mixture = 10 litre

Alcohol in the mixture = 10 × 1/5 = 2 litre

Quantity of alcohol taken out from mixture = 1/5 × M = M/5 litre

Remaining alcohol in the mixture = 2 – M/5

⇒ 1/5 × 10 – 1/5 × M = 1/10 × 10

⇒ M = 5

∴ Then, 5 litres of water is added.

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