Question

A can finish a work 12 days and B can do it in 15. after A had worked for 3 days, B also joined a to finish the remaining work. How many days they will take to complete the work together?

Answer 1

Person                    days                             portion of work
A                              12                                    1(whole)
A                               1                                    1/12
A                               3                                     3/12 = 1/4
A                               d                                       d/12
B                              15                                      1 (whole)
B                               1                                       1/15
B                                d                                      d/15

where, d is the no of days taken by A and B to complete left portion

left portion of work = 1 - 3/12 = 1- 1/4 = 3/4 (1/4 finished by A)

now A and B work together

 3/4 = d/12 + d/15

⇒ 3/4 = 5d + 4d / 60 = 9d/60  ⇒ d = 3 x 60 / 4 x 9 = 5

So they'll take 5 days more to finish the task.