A can complete a piece of work in 10 days, while B can complete the same work…
2026
A can complete a piece of work in 10 days, while B can complete the same work in 12 days. If they work together, how many days will they take to complete one-eighth of the work?
Answer: C. 15/22 days — ConceptIf a person completes one whole job in d days, that person’s work rate is 1/d of the job per day. For people working together, add their rates. The…
- A.
12/17 days
- B.
14/19 days
- C.
15/22 days
- D.
11/14 days
Attempted by 47 students.
Show answer & explanation
Correct answer: C
Concept
If a person completes one whole job in d days, that person’s work rate is 1/d of the job per day.
For people working together, add their rates. The time for a required fraction of the job equals that fraction divided by the combined rate.
Application
A’s rate is 1/10 of the work per day, and B’s rate is 1/12 of the work per day.
Their combined rate is 1/10 + 1/12 = 6/60 + 5/60 = 11/60 of the work per day.
Let t be the number of days needed for 1/8 of the work. Then (11/60)t = 1/8.
Therefore, t = (1/8) ÷ (11/60) = (1/8) × (60/11) = 15/22 day.
Cross-check
In 15/22 day, the completed work is (11/60) × (15/22) = 1/8, so the required fraction is obtained.
Result
Thus, they will take 15/22 day.