Sharing the payment — Time & Work Aptitude Question
Sharing the payment: A can do a work in 6 days and B in 8 days. With C's help they finish it in 3 days and are paid… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 135 seconds
Question
A can do a work in 6 days and B in 8 days. With C's help they finish it in 3 days and are paid ₹600 in all. What is C's share?
Options
- ₹50
- ₹75
- ₹100
- ₹150
Show the answer and the worked solution
Correct answer: B. ₹75
Worked solution
- Combined rate = 1/3. A + B = 1/6 + 1/8 = 4/24 + 3/24 = 7/24.
- C's rate = 8/24 − 7/24 = 1/24.
- C's share of the work = (1/24) ÷ (1/3) = 1/8.
- C's payment = 600 ÷ 8 = ₹75.
Answer: ₹75.
The idea
Wages divide in the ratio of work completed, which is the ratio of the rates. Find each rate, then take each person's fraction of the total.
Shortcut. In the 3 days A does 3/6 = 1/2 and B does 3/8, so C's part is 1 − 1/2 − 3/8 = 1/8, and 600 ÷ 8 = ₹75.
Common trap. Paying C his one-day fraction — 1/24 of ₹600 = ₹25 — forgets that he works all 3 days; his part of the job is 3 × 1/24 = 1/8, so he earns an eighth of the ₹600.