Half the work, a third of the work — Aptitude Question
Half the work, a third of the work: A does half a job in 5 days; B does one-third of the same job in 5 days. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
A does half a job in 5 days; B does one-third of the same job in 5 days. How long will they take together to complete it?
Options
- 5 days
- 6 days
- 7.5 days
- 9 days
Show the answer and the worked solution
Correct answer: B. 6 days
Worked solution
- A does 1/2 in 5 days, so the whole job would take 10 days.
- B does 1/3 in 5 days, so the whole job would take 15 days.
- Together: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6.
- Time = 6 days.
Answer: 6 days.
The idea
Scale each partial job up to a whole-job time first, then add the rates. Adding the two partial times directly is meaningless.
Shortcut. In 5 days together they finish 1/2 + 1/3 = 5/6 of the job, so the whole takes 5 × 6/5 = 6 days.
Common trap. 5 days — treating a half plus a third as the whole job; 1/2 + 1/3 = 5/6 leaves a sixth undone.