A can finish the work in 25 days and B in 25 days. They both work together for…
20172017
A can finish the work in 25 days and B in 25 days. They both work together for 5 days and then B leaves. How many more days will A take to complete the remaining work?
- A.
18 days
- B.
20 days
- C.
15 days
- D.
17 days
Attempted by 79 students.
Show answer & explanation
Correct answer: C
Concept
Work-and-time problems use rates: if a worker finishes a job in n days, that worker's one-day rate is 1/n of the job. Rates add when people work together, and Work done = rate × time. The remaining fraction of the job is 1 minus the fraction already completed, and time for one worker to finish it equals remaining work ÷ that worker's rate.
Application
A's one-day rate = 1/25 of the job; B's one-day rate = 1/25 of the job.
Combined one-day rate = 1/25 + 1/25 = 2/25 of the job.
Work done together in 5 days = 5 × 2/25 = 10/25 = 2/5 of the job.
Remaining work = 1 − 2/5 = 3/5 of the job.
A finishes the remaining 3/5 alone: time = (3/5) ÷ (1/25) = (3/5) × 25 = 15 days.
Cross-check
In 15 days A does 15 × (1/25) = 15/25 = 3/5 of the job, which is exactly the remaining work. Adding the 2/5 done in the first 5 days gives 2/5 + 3/5 = 1 (the whole job), so 15 days is consistent.