From a vessel, 1/3rd of the liquid evaporates on the first day. On the second…
2023
From a vessel, 1/3rd of the liquid evaporates on the first day. On the second day 3/4th of the remaining liquid evaporates. What fraction of the volume is present at the end of the second day?
- A.
1/12
- B.
1/8
- C.
1/6
- D.
1/5
Show answer & explanation
Correct answer: C
The fraction of a quantity remaining after a fractional loss is the previous remaining fraction multiplied by (1 minus the fraction lost in that step) — successive fractional losses multiply together, they do not simply add.
Let the initial volume of liquid in the vessel be 1 (the whole).
On the first day, 1/3 of the liquid evaporates, so the fraction remaining is 1 − 1/3 = 2/3.
On the second day, 3/4 of the remaining liquid (2/3) evaporates, so the fraction remaining after the second day is 2/3 × (1 − 3/4) = 2/3 × 1/4 = 1/6.
Cross-check: total fraction evaporated = 1/3 (day 1) + (3/4 × 2/3) (day 2) = 1/3 + 1/2 = 5/6, so remaining = 1 − 5/6 = 1/6, matching the step-by-step result.
So 1/6 of the volume is present at the end of the second day.