A container initially holds 80 litres of a mixture of milk and water in the ratio 3:1. From this container, 16 litres of the mixture is removed and replaced entirely with pure water. This process is repeated one more time. What is the final quantity of milk (in litres) remaining in the container?
Show answer & explanation
Correct answer: B
Explanation
Given:
Milk : Water = 3 : 1
Total mixture = 80 liters
Mixture withdrawn = 16 liters (twice)
According to the formula:
Remaining milk = Initial milk × (1 − Amount withdrawn / Total)ⁿ
Initial milk = (3/4) × 80 = 60 liters
Ratio = 1 − 16/80 = 4/5
Process repeated twice:
Remaining milk = 60 × (4/5)²
= 60 × 16/25
= 960/25
= 38.4 liters