Question

A and b can do a piece of work in 12 days and 15 days respectively while c can destroy the same work in 20 days. in how many days the work will be completed if a start the work from first day followed by b on second day and then followed by c on third day and so on..?

Answer 1

A can do 1 work in 12 days
A in 1 day does: 1/12 work
B can do 1 work in 15 days
B in 1 day does: 1/15 work
C can destroy 1 work in 20 days
C in 1 day destroys: -1/20 work [-ve sign since C is destroying]
They works alternatively. So 1 cycle is completed in 3 days(A,B,C)

In 3 days, work done:
1/12 + 1/15 - 1/20 = 5+4-3/60 = 6/60 = 1/10 work.
3 days=== 1/10 work

3days* 9 === 9*1/10
27 days=== 9/10 work
Work Remaining = 1/10 or 6/60

Next A's turn"
1 day == 1/12 work or 5/60
Now work remaining after 28 days = 1/60
Next B's turn 
1 day == 4/60
x === 1/60
4x/60 = 1/60
x = 1/4 days.
Hence the work will be completed in 28 1/4 days.
Hope it helps.