If A and B work together , they will complete a job in 7.5 days. However, if A…
2023
If A and B work together , they will complete a job in 7.5 days. However, if A works alone and completes half of the work and then B takes over and complete the remaining half alone , they will take 20 days . How long will B alone takes to do the work if A is more efficient than B?
- A.
40 days
- B.
30 days
- C.
20 days
- D.
10 days
Attempted by 13 students.
Show answer & explanation
Correct answer: B
Solution:
Let A take a days and B take b days to complete the whole job alone.
Working together they finish in 7.5 days, so their combined rate is 1/a + 1/b = 1/7.5 = 2/15.
If A does half the job and B does the other half, total time = a/2 + b/2 = 20, so a + b = 40.
Use (a + b)/ab = 2/15. With a + b = 40, we get 40/ab = 2/15, so ab = 300.
Solve x^2 - 40x + 300 = 0 to find the individual times: the roots are x = 10 and x = 30.
Since A is more efficient, A = 10 days and B = 30 days. Therefore B alone takes 30 days.