Working on alternate days — Time & Work Aptitude Question
Working on alternate days: A can do a job in 10 days and B in 15 days. They work on alternate days, A starting first. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 90 seconds
Question
A can do a job in 10 days and B in 15 days. They work on alternate days, A starting first. In how many days is the job finished?
Options
- 11
- 12
- 12.5
- 13
Show the answer and the worked solution
Correct answer: B. 12
Worked solution
- Work = 30 units. A does 3 units on his day, B does 2 on his.
- Each 2-day cycle completes 5 units; 30/5 = 6 cycles exactly.
- 6 cycles = 12 days, and the job ends precisely at the close of B's sixth day.
Answer: 12 days.
The idea
For alternate-day work, find the work per cycle and count whole cycles; then handle any remainder day by day, in order, checking who works that day. Here there is no remainder, which is where many candidates add an extra day by reflex.
Shortcut. Together they would take 6 days (10 × 15 ÷ 25); alternating halves the pace, so 12 days — exact because 6 is a whole number.
Common trap. 13 — adding a final day out of habit, as if work remained after the sixth A–B cycle; 6 cycles of 5 units finish the 30 exactly.