Question

The ratio of rum and whiskey in a solution is 4 ∶ 5. The ratio is changed to 2 ∶ 1 when 27 litres of the solution is replaced with rum. What is the amount of rum in the original solution?
1. 22.5 litres
2. 30 litres
3. 37.5 litres
4. 45 litres

Answer 1

Correct Answer - Option 2 : 30 litres

Given:

Ratio of rum and whiskey = 4 ∶ 5

Ratio when solution replaced with 27 litres of rum = 2 ∶ 1

Calculations:

Let the amount of rum and whiskey in the original solution be 4x and 5x

When the solution was replaced,

Amount of rum in new solution = 4x – 27 × (4/9) + 27

⇒ 4x + 27 × (5/9)

⇒ 4x + 15

Amount of whiskey in new solution = 5x – 27 × (5/9)

⇒ 5x – 15

Ratio in the new solution = (4x + 15)/(5x – 15)

⇒ (4x + 15)/(5x – 15) = 2

⇒ 4x + 15 = 10x – 30

⇒ 6x = 45

⇒ x = 7.5 litres

Amount of rum in original solution = 4 × 7.5 = 30 litres

∴ The amount of rum in original solution is 30 litres