In a vessel , there are 20 litres of alcohol . An operation is defined as…
2024
In a vessel , there are 20 litres of alcohol . An operation is defined as taking out five litres of what is present in the vessel and adding 5 litres of pure water to it . What is the ratio of alcohol to water after two operatons?
- A.
5:7
- B.
2:3
- C.
9:7
- D.
3/7
Attempted by 452 students.
Show answer & explanation
Correct answer: C
Answer: 9 : 7
Key idea: Each operation removes 5 litres out of 20, i.e. removes 1/4 of the mixture. So the fraction of alcohol remaining after one operation is 1 - 1/4 = 3/4. Repeating the operation multiplies the alcohol amount by 3/4 again.
Alcohol after two operations = 20 * (3/4)^2 = 20 * 9/16 = 45/4 litres.
Water after two operations = total - alcohol = 20 - 45/4 = 35/4 litres.
Ratio alcohol : water = (45/4) : (35/4) = 45 : 35 = 9 : 7.
Alternate sequential method:
After 1st operation: remove 5 L alcohol → alcohol = 20 - 5 = 15 L, water = 5 L.
After 2nd operation: remove (5/20)*15 = 75/20 = 15*1/4 = 15/4 L alcohol, so remaining alcohol = 15 - 15/4 = 45/4 L; water = 20 - 45/4 = 35/4 L.
Hence the required ratio is 9 : 7.