Question

A mixture contains Alcohol and water in the ratio 7 : 5. When 5 litres of water and 6 litres of alcohol is added to the mixture, the ratio of alcohol to water in the resultant mixture becomes 34 : 25. Find the initial quantity of the mixture.

1. 189 litres
2. 190 litres
3. 48 litres
4. 58 litres
5. None of these.

Answer 1

Correct Answer - Option 3 : 48 litres

Given:

Initial ratio = 7 : 5

Amount of water added = 5 litres

Amount of alcohol added = 6 litres

Final ratio of mixture = 34 : 25

Calculation:

Let the initial quantity of alcohol and water be 7x and 5x respectively.

After adding 6 litres of alcohol and 5 litres of water,

⇒ New mixture contains alcohol and water (7x + 6) and (5x + 5) respectively.

⇒ (7x + 6)/(5x + 5) = 34/25

⇒ 175x + 150 = 170x + 170

⇒ 175x – 170x = 170 – 150

⇒ 5x = 20

⇒ x = 4

∵ Initial quantity of Alcohol is 7x.

⇒ 7 × 4

⇒ 28 litres

∵ Initial quantity of Water is 5x.

⇒ 5 × 4

⇒ 20 litres

Initial quantity = 28 + 20

⇒ 48 litres

∴ Initial quantity of mixture is 48 litres.