A can finish the work in 30 days and B in 40 days. They both work together for…
2017
A can finish the work in 30 days and B in 40 days. They both work together for 5 days and then B leaves. How many days will A take to complete the remaining work?
- A.
22 days
- B.
21.75 days
- C.
21.25 days
- D.
21 days
Attempted by 6 students.
Show answer & explanation
Correct answer: C
Concept
In work-rate problems, each worker's one-day output is the reciprocal of the time they take alone. Outputs add when people work together, the total job equals 1 (or, conveniently, the LCM of the individual times in "units"), and remaining time equals remaining work divided by the rate of whoever finishes it.
Application
Take the total work as the LCM of 30 and 40, which is 120 units. Then A does 120/30 = 4 units per day and B does 120/40 = 3 units per day.
Working together, their combined output is 4 + 3 = 7 units per day. Over 5 days they complete 7 x 5 = 35 units.
Work still left after B leaves = 120 - 35 = 85 units.
A finishes this alone at 4 units per day, so the time needed = 85 / 4 = 21.25 days.
Cross-check
Using fractions instead of units: in 5 days the pair completes 5 x (1/30 + 1/40) = 5 x 7/120 = 7/24 of the job, leaving 17/24. A alone needs (17/24) / (1/30) = (17/24) x 30 = 21.25 days, which matches.