Question

mary alone can finish a painting job in 12 days. Gary alone can do the same job in 20 days. Mary work alone for 4 days and Gary joins to help. In how many days they will they finish the job.

Answer 1

Work one by Mary in the first 4 days :  4* 1/12 = 1/3
Work remaining = 1 - 1/3 = 2/3

Combined productivity of both = 1/12 + 1/20 = 8/60 = 2/15

They take  2/3 / (2/15)  =  2/3 * 15/2 = 5 days
 
So they take 5 days to finish the job after Mary works alone for 4 days.