There is a cask full of milk. E litres of milk are drawn from the cask and…
2025
There is a cask full of milk. E litres of milk are drawn from the cask and replaced with water. this process is repeated. now ratio of milk and water is 16:9. what is the capacity of the cask in litres?
- A.
E+9
- B.
5E
- C.
9E
- D.
cannot be determined
Attempted by 13 students.
Show answer & explanation
Correct answer: B
Solution:
Let C be the capacity of the cask (in litres). Each time E litres are removed and the cask is refilled, the fraction of milk remaining is multiplied by (1 - E/C).
After the first replacement the milk fraction is 1 - E/C.
After the second replacement the milk fraction is (1 - E/C)^2.
Given the final ratio of milk to water is 16:9, the milk fraction is 16/25. Therefore (1 - E/C)^2 = 16/25.
Taking the positive square root (since 1 - E/C > 0): 1 - E/C = 4/5. Thus E/C = 1/5 and C = 5E.
Note: This derivation assumes the process was repeated twice. If the number of repetitions n is not specified, the capacity cannot be uniquely determined from the given final ratio alone; in the general case one would have (1 - E/C)^n = 16/25, so C = E / (1 - (16/25)^(1/n)).