Work problems

Question

B, K and M can do a piece of work in 18 days, 27 days and 36 days. They started working Together. After working for 4 days, B goes away and K leaves 7 days before the work is finishe. Only M remains at work from the beginning to the end. In how many days was the whole work done? 

 

Can anyone please give me the shortest method to solve problems like these 

Answer 1

In the first four days:

4/18 + 4/27 + 4/36

24+/108 + 16/108 + 12/108

52/108 of the job has been completed

 

In the last 7 days M does 7/36, or 21/108

52/108 + 21/108 

73/108 is completed

35/108 is done by K and M.

x/27 + x/36 = 35/108

4x + 3x = 35                 LCD 35

7x = 35

x = 5

 

Total time, 4 days (the start) + 5 days (K & M) + 7 days (M alone)