Question

In 120 litres pure alcohol, 12 liters of alcohol is replaced by water if this process is repeated two more times then what will be the quantity of alcohol in the final mixture?

1. 87.48 litres
2. 84.48 litres
3. 80 litres
4. 90 litres

Answer 1

Correct Answer - Option 1 : 87.48 litres

Given:

Quantity of pure alcohol = 120 liters

Formula used:

Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations,

Quantity of pure liquid in the final mixture = x {1 – (y/x)}ⁿ

Calculation:

Quantity of pure liquid in the final mixture = x {1 – (y/x)}ⁿ

⇒ Quantity of pure alcohol in the final mixture = 120 × {1 – (12/120)}³

⇒ Quantity of pure alcohol in the final mixture = 120 × (9/10)³

⇒ Quantity of pure alcohol in the final mixture = 120 × (729/1000)

⇒ Quantity of pure alcohol in the final mixture = 120 × (729/1000)

⇒ Quantity of pure alcohol in the final mixture = 87.48

∴ The final quantity of the alcohol is 87.48 liters.