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In a mixture of 30 litres, alcohol and water are in the ratio of 3 : 2. If 20 litres of mixture is removed and then 15 litres of alcohol and 10 litres of water is added to the mixture. What is the ratio of alcohol and water in the new mixture?

In a mixture of 30 litres, alcohol and water are in the ratio of 3 : 2. If 20 litres of mixture is removed and then 15 litres of alcohol and 10 litres of water is added to the mixture. What is the ratio of alcohol and water in the new mixture? Correct Answer 3 : 2

Given:

Initial quantity of mixture = 30 litres

Initial ratio of alcohol and water = 3 : 2

Amount of mixture removed = 20 litres

Amount of alcohol added = 15 litres

Amount of water added = 10 litres

Calculations:

Let the initial quantity of alcohol and water be 3x and 2x respectively.

After removal of 20 litres of mixture,

Remaining quantity of mixture = 30 – 20

⇒ 10 litres

∵ Ratio of alcohol and water will remain same after removal of mixture,

3x + 2x = 10

⇒ 5x = 10

⇒ x = 2

Now, remaining amount of alcohol in the mixture = 3x

⇒ 3 × 2

⇒ 6 litres

Remaining amount of water in the mixture = 2x

⇒ 2 × 2

⇒ 4 litres

After addition of 15 litres of alcohol and 10 litres of water,

New amount of alcohol = 6 + 15

⇒ 21 litres

New amount of water = 4 + 10

⇒ 14 litres

Ratio of new amount of alcohol to new amount of water = 21 : 14

⇒ 3 : 2

∴  The ratio of alcohol and water in the new mixture = 3 : 2

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