C's help finishes it in four days — Aptitude Question
C's help finishes it in four days: A alone takes 8 days and B alone 12 days. With C's help they finish the work in… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A alone takes 8 days and B alone 12 days. With C's help they finish the work in 4 days. How long would C alone take?
Options
- 16 days
- 20 days
- 24 days
- 30 days
Show the answer and the worked solution
Correct answer: C. 24 days
Worked solution
- 1/4 = 6/24, 1/8 = 3/24, 1/12 = 2/24.
- C's rate = 6/24 − 3/24 − 2/24 = 1/24.
- C alone takes 24 days.
Answer: 24 days.
The idea
Subtract the known rates from the combined rate. Choosing the LCM of the given times as the denominator keeps every step in whole numbers.
Shortcut. In the 4 days A does 4/8 = 1/2 and B 4/12 = 1/3, leaving C 1/6 of the job in 4 days — so C alone needs 24.
Common trap. 20 days — adding A's and B's times (8 + 12); times never add, and C's rate is 1/4 − 1/8 − 1/12 = 1/24.