Five pipes P, Q, R, S, and T can fill a tank in 60 minutes, 20 minutes, 30 minutes, 8 minutes, 32 minutes respectively. Out of these five pipes, two have now been converted into emptying pipes such that their efficiency remains the same. When only one of the filling pipes and one of the emptying pipes operate, the tank can be filled in 60 minutes while another combination of emptying and filling pipe empties it in 8/45th of the time taken by the previous combination to fill the tank. Which pipes are converted into emptying pipes?

Option 4 : Cannot be determined

Calculation:

Let the total work be done is 480 units (L.C.M of 60, 20, 30, 8, 32)

∴ respective efficiencies of different pipes are:

⇒ Pipe P: 8 units (480/60)

⇒ Pipe Q: 24 units (480/20)

⇒ Pipe R: 16 units (480/30)

⇒ Pipe S: 60 units (480/8)

⇒ Pipe T: 15 units (480/32)

Now, one combination of emptying and filling pipe can fill the tank in 60 minutes.

∴ together they can do 480/60

⇒ 8 units of work per day.

Out of the combinations possible, only P-R and Q-R have a difference of 8 units/min.

So, if P is emptying the tank and R is a filling then they will do 8 units of work per min.

When R is emptying the tank and Q is filling then they will do 8 units of work per min.

According to the question, the second combination takes 8/45^th of the time of the first one. i.e. 32/3 minutes.

But the only combination that does this is when S is the emptying pipe and T is the filling pipe.

∴ among P, Q, and R, we cannot know for sure which pipe is the filling one and which is the emptying one.