Alternate days: 20 and 30 days — Aptitude Question
Alternate days: 20 and 30 days: A can complete a work in 20 days and B in 30 days. They work on alternate days,… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A can complete a work in 20 days and B in 30 days. They work on alternate days, with A starting. In how many days is the work finished?
Options
- 22 days
- 24 days
- 25 days
- 26 days
Show the answer and the worked solution
Correct answer: B. 24 days
Worked solution
- Work = 60 units. A does 3 units on his day, B does 2 on his.
- Each 2-day cycle = 5 units, and 60 ÷ 5 = 12 cycles exactly.
- 12 cycles = 24 days.
Answer: 24 days.
The idea
Find the work per cycle, count the whole cycles, then handle any remainder day by day in the correct order. Here it divides exactly, so no remainder arises.
Shortcut. Two alternate days equal one joint day. The pair together need 20 × 30 ÷ 50 = 12 days, a whole number, so alternation takes exactly 24.
Common trap. 25 days — adding a day for A to finish off, without noticing that the 12 two-day cycles land exactly on the whole job.