A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes

A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?

(1)          23

(2)          44

(3)          29

(4)          42

a)            1 and 2 only

b)            1 and 3 only

c)            2 and 4 only

d)            2 and 3 only 23.

Sol:

2 fill pipes cancel out 3 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5 hours. so the answer has to be 5k + 4.

Both 44 and 29 are possible.