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.