A beaker contains 180 liters of alcohol. On first day, 60 liters of alcohol is…
2024
A beaker contains 180 liters of alcohol. On first day, 60 liters of alcohol is taken out and replaced by water. Second day, 60 liters of mixture is taken out and replaced by water and the process continues day after day. What will be the quantity of alcohol in beaker after 3 days ?
- A.
30 litres
- B.
64.8 litres
- C.
53.3 litres
- D.
108 litres
Attempted by 22 students.
Show answer & explanation
Correct answer: C
Key formula: Final amount = Initial amount × (1 - replaced/total)^n
Initial amount of alcohol = 180 litres.
Each day 60 litres are removed and replaced by water, so the fraction of alcohol remaining each day is 1 - 60/180 = 2/3.
After 3 days the remaining fraction = (2/3)^3 = 8/27 ≈ 0.296296...
Final amount = 180 × 8/27 = 180 × 0.296296... = 53.333... litres ≈ 53.3 litres.
Answer: 53.3 litres.