B leaves partway — Time & Work Aptitude Question
B leaves partway: A and B together can do a work in 30 days. They work together for 20 days, then B leaves and A… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A and B together can do a work in 30 days. They work together for 20 days, then B leaves and A finishes the rest in 20 more days. How long would A alone take for the whole work?
Options
- 45 days
- 50 days
- 60 days
- 75 days
Show the answer and the worked solution
Correct answer: C. 60 days
Worked solution
- In 20 days the pair complete 20/30 = 2/3 of the work.
- A does the remaining 1/3 in 20 days.
- So A alone would take 20 × 3 = 60 days.
Answer: 60 days.
The idea
Convert the leftover fraction and its time into a full-job time by simple scaling. B's individual rate is never needed.
Shortcut. The pair would have finished the last third in 10 days; A alone took 20, so A works at half the pair's rate and needs 2 × 30 = 60 days.
Common trap. 50 days — adding A's extra 20 days to the pair's 30, as if the solo stint only stretched the schedule; those 20 days cover just the last third.