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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?

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? Correct Answer 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

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