A leaves after four days — Time & Work Aptitude Question
A leaves after four days: A and B can finish a job in 10 and 15 days respectively. They start together, but A… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A and B can finish a job in 10 and 15 days respectively. They start together, but A leaves after 4 days. How many more days does B need to finish?
Options
- 4
- 5
- 6
- 7.5
Show the answer and the worked solution
Correct answer: B. 5
Worked solution
- Let the job be 30 units (LCM of 10 and 15). A does 3 units/day, B does 2.
- Together for 4 days: 4 × 5 = 20 units done; 10 remain.
- B alone at 2 units/day needs 10/2 = 5 days.
Answer: 5 days.
The idea
Choose the LCM of the given times as the total work so every rate is a whole number. Then it is bookkeeping: work done, work left, divide by the rate that continues.
Shortcut. A's 4 days do 4/10 of the job; B does the other 6/10, which takes him 0.6 × 15 = 9 days in all — 4 of them already worked, so 5 more.
Common trap. 7.5 — half of B's 15 days, as if the 4 days together had done only half the job; they did 4 × (1/10 + 1/15) = 2/3, leaving a third for B.