A and B together complete one unit of work in 2 days. A alone can complete the…
2026
A and B together complete one unit of work in 2 days. A alone can complete the same work in 12 days. How many days will B alone take to complete 80 times that work?
Answer: A. 192 — ConceptWork rate is the fraction of one job completed per day. If workers act together, their individual rates add. For a worker with daily rate r, the time…
- A.
192
- B.
193
- C.
96
- D.
112
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Show answer & explanation
Correct answer: A
Concept
Work rate is the fraction of one job completed per day. If workers act together, their individual rates add.
For a worker with daily rate r, the time needed for W units of work is W divided by r.
Application
The combined rate of A and B is 1/2 work per day.
A's rate is 1/12 work per day.
Therefore, B's rate is 1/2 minus 1/12 = 6/12 minus 1/12 = 5/12 work per day.
For 80 units of work, B's time is 80 divided by (5/12) = 80 multiplied by (12/5) = 192 days.
Cross-check
In 192 days, B completes 192 multiplied by 5/12 = 80 units of work, which matches the required amount.
Result
B alone takes 192 days.