In a barrel 729 ml of oil. N amount of oil is replaced by water. If the…
2024
In a barrel 729 ml of oil. N amount of oil is replaced by water. If the process continues for the 6 times and find the amount of oil will be?
- A.
729(1-n/729)^6
- B.
(729-n/729)^6
- C.
729(1-n/729)^4
- D.
729(1-(n/729)^2)^3
Attempted by 6 students.
Show answer & explanation
Correct answer: A
Solution: Derivation of the remaining oil after repeated replacement.
Start with 729 ml of pure oil.
When n ml of the mixture is removed, the fraction of the barrel removed is n/729. Therefore the fraction of oil that remains after one replacement is (1 - n/729).
Each successive replacement multiplies the remaining oil by the same factor (1 - n/729). After k replacements the remaining oil is 729*(1 - n/729)^k.
For k = 6 replacements, the amount of oil left is 729*(1 - n/729)^6.
Final answer: 729*(1 - n/729)^6