Question

# A drain pipe can drain a tank in 12 hours, and a fill pipe can fill the same tank in 6 hours. A total of n pipes – which include a few fill pipes and the remaining drain pipes – can fill the entire tank in 2 hours. How many of the following values could ‘n’ take

CAT 2021

Correct option is

**Explanatory Answer**

The two drain pipes can drain the same volume that one fill pipe fills , which mens that a D-D-F combination has to have a net volume effect of 0

hence only the fills pipes can manage to fill the tank . as we want all the net zero effect pipes , we want three more fill pipes to fill the tank in 2 hours

so , we can have as many D-D-Fs as we want , but we need one F-F-F at the end to ensure tank to fill in 2 hrs

then the no. of pipes will be (D- D-F).....(D- D-F) + (F- F-F)

hence we can say that no. of pipes should be multiple of 3.

so , A option is correct.