A vessel contains 120 litres of juice. 20% of the juice is taken out and the…
2025
A vessel contains 120 litres of juice. 20% of the juice is taken out and the same is repeated two more times. Water of the amount equal to the juice taken out is mixed with the remaining juice in the vessel. what is the ratio of the juice and water in the vessel?
- A.
4/9
- B.
12/15
- C.
16/9
- D.
9/16
Attempted by 10 students.
Show answer & explanation
Correct answer: B
Solution:
Start with 120 litres of pure juice.
Each removal takes out 20% of the current juice and the removed amount is replaced with water, so the remaining juice is multiplied by (1 − 0.2) = 4/5 each time.
After three such repetitions the juice volume = 120 × (4/5)^3 = 120 × 64/125 = 1536/25 = 61.44 litres.
Water volume = total − juice = 120 − 61.44 = 1464/25 = 58.56 litres.
Therefore juice : water = 1536/25 : 1464/25 = 1536 : 1464 = 64 : 61.
Note: None of the provided options equal 64:61. The option with value 12/15 (which equals 4/5) is the fraction after a single removal and is not the final answer; the question's marked correct option is therefore incorrect.