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55 litres of a solution contains alcohol and water in the ratio 2 : 3. Water is added in the solution. The new mixture has a ratio of alcohol and water as 1 : 5. Find the quantity of water added.


1. 87 litres
2. 97 litres
3. 67 litres
4. 77 litres
5. None of these.

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Correct Answer - Option 4 : 77 litres

Given:

Initial quantity of mixture = 55 litres

Initial ratio of mixture = 2 : 3

Final ratio of mixture = 1 : 5

Calculation:

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

⇒ 2x + 3x = 55

⇒ 5x = 55

⇒ x = 11

Initial quantity of alcohol = 2x

⇒ 22 litres

Initial quantity of water = 3x

⇒ 33 litres

Let the water to be added be x litres.

22/(33 + x) = 1/5

⇒ 110 = 33 + x

⇒ 77 = x

Quantity of water added is 77 litres.

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