Three times as good, sixty days sooner — Aptitude Question
Three times as good, sixty days sooner: A is three times as good a workman as B and takes 60 days less than B to… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A is three times as good a workman as B and takes 60 days less than B to finish a job. How long do they take working together?
Options
- 20 days
- 22.5 days
- 25 days
- 30 days
Show the answer and the worked solution
Correct answer: B. 22.5 days
Worked solution
- Let A take x days, so B takes 3x days. Then 3x − x = 60 → x = 30.
- A takes 30 days, B takes 90 days.
- Together: 1/30 + 1/90 = 3/90 + 1/90 = 4/90 = 2/45.
- Time = 45/2 = 22.5 days.
Answer: 22.5 days.
The idea
Three times as efficient means one third of the time, not three times the time. Fixing that relation first is the whole difficulty here.
Shortcut. Times are in the ratio 1 : 3, so the 60-day gap is 2 parts: A 30, B 90. Together = 30 × 90 ÷ 120 = 22.5 days.
Common trap. 30 days — A's time alone, stopping before combining the two rates.