Question 761369
Let the tank's capacity be C.

P1 takes 45 min to fill the tank. So in 1 minute, P1 will fill 1/45 of the tank.

Similarly, in 1 minute, P2 will fill 1/30 of the tank.

Together, in 1 minute, they will fill out {{{1/45 + 1/30 = 5/90 = 1/18}}} of the tank.

So, together, they will take 18 minutes to fill the tank - if there was no drainage.

But because of the drainage, they take 27 min. So the effective rate of filling is not 1/18 but 1/27 per min.

Effective rate = Rate of P1 + Rate of P2 - Rate of P3 (drainage pipe)

Substituting,

{{{1/27 = 1/45 + 1/30 - P3}}}

P3 = {{{1/18 - 1/27 = 1/54}}}

i.e. P3 empties 1/54 of the tank every minute.

So it would take P3 54 minutes to empty a full tank.

:)