A can finish the work in 15 days and B in 30 days. They both work together for…
2017
A can finish the work in 15 days and B in 30 days. They both work together for 5 days and then B leaves. How many days will A take to complete the remaining work?
- A.
7.75 days
- B.
7 days
- C.
7.5 days
- D.
7.45 days
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Concept
When several workers act together, their one-day work rates ADD UP. If a worker finishes a job in n days, that worker's one-day rate is 1/n of the job. Treat the whole job as 1 unit, find the fraction done in the given period, subtract from 1 to get the remaining fraction, then divide that remaining fraction by the rate of whoever finishes it.
Application
A's one-day rate = 1/15 of the job; B's one-day rate = 1/30 of the job.
Combined one-day rate of A and B = 1/15 + 1/30 = 2/30 + 1/30 = 3/30 = 1/10 of the job.
Work done together in 5 days = 5 × 1/10 = 5/10 = 1/2 of the job.
Remaining work = 1 − 1/2 = 1/2 of the job.
A finishes this alone at 1/15 per day, so time = (1/2) ÷ (1/15) = (1/2) × 15 = 15/2 = 7.5 days.
Cross-check
In 7.5 days A alone does 7.5 × 1/15 = 7.5/15 = 1/2 of the job. Added to the 1/2 already completed in the first 5 days, the total is exactly 1 whole job, which confirms the result.