A leaves five days before the end — Aptitude Question
A leaves five days before the end: A can do a work in 20 days and B in 30 days. They begin together, but A leaves 5… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
A can do a work in 20 days and B in 30 days. They begin together, but A leaves 5 days before the work is finished. In how many days is the work completed?
Options
- 12 days
- 15 days
- 18 days
- 20 days
Show the answer and the worked solution
Correct answer: B. 15 days
Worked solution
- Let the total time be T days. Then (T − 5)/20 + T/30 = 1.
- Multiply by 60: 3(T − 5) + 2T = 60 → 3T − 15 + 2T = 60 → 5T = 75.
- T = 15 days.
Answer: 15 days.
The idea
Set up one equation in the total time, remembering that the person who leaves works fewer days. The one who stays always works the full duration.
Shortcut. Pretend A stays to the end: he would add 5/20 = 1/4 of a job, so the pair (12 days a job, 20 × 30 ÷ 50) would finish 1¼ jobs in the time: 1.25 × 12 = 15 days.
Common trap. 12 days — the time if both worked throughout, ignoring that A leaves early.