A, B and C can do a piece of work in 12 days, 15 days and 16 days,…
2026
A, B and C can do a piece of work in 12 days, 15 days and 16 days, respectively. If A, B and C work together, then how many days will they take to complete the work?
Answer: D. 4 12/17 days — ConceptWhen people work independently on the same job, their work rates add. If the combined rate is R jobs per day, the completion time is 1/R days.…
- A.
3 14/15 days
- B.
3 11/19 days
- C.
2 10/13 days
- D.
4 12/17 days
Attempted by 25 students.
Show answer & explanation
Correct answer: D
Concept
When people work independently on the same job, their work rates add. If the combined rate is R jobs per day, the completion time is 1/R days.
Application
A, B and C complete 1/12, 1/15 and 1/16 of the work per day, respectively.
Using 240 as the common denominator, the combined rate is 20/240 + 16/240 + 15/240 = 51/240 = 17/80 of the work per day.
Therefore, the required time is 1 ÷ (17/80) = 80/17 = 4 12/17 days.
Cross-check
Multiplying the combined rate by the computed time gives (17/80) × (80/17) = 1 complete job.
Thus, A, B and C together complete the work in 4 12/17 days.