A and B working together — Time & Work Aptitude Question
A and B working together: A can finish a job in 12 days and B in 18 days. Working together, how long do they take? Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
A can finish a job in 12 days and B in 18 days. Working together, how long do they take?
Options
- 6 days
- 7.2 days
- 7.5 days
- 8 days
Show the answer and the worked solution
Correct answer: B. 7.2 days
Worked solution
- A does 1/12 per day, B does 1/18 per day.
- Together: 1/12 + 1/18 = 3/36 + 2/36 = 5/36 per day.
- Time = 36/5 = 7.2 days.
Answer: 7.2 days.
The idea
Work in rates, not times. Or take the total work as the LCM of the times (36 units): A does 3 a day, B does 2, together 5, so 36/5 days. The LCM method avoids fractions entirely.
Shortcut. For two workers, time together = product ÷ sum = 12 × 18 ÷ 30 = 216 ÷ 30 = 7.2 days.
Common trap. 7.5 days — averaging the times to 15 days and halving, as if both were 15-day workers; the faster worker counts for more, pulling the time below 7.5.