Pipes A, B and C can fill a tank in 30, 60 and 90 min respectively. Pipe A and C are kept open for 12 min and after that pipe A stop working and pipe B is opened. Pipe C stop working 8 min before the tank is full. How long does C and B work together?

12 min

A  :  B  :  C

30 : 60 : 90    Time

Let the total work be 180

So ratio of efficiency = 6  :  3  :  2

Now,

i) Work done by (A + C) in 12 mins  = 12 x 8 = 96

ii) Work done by B alone in last 08 mins = 3 x 8 = 24

Total work done in (i) and (ii) = 96 +24 = 120

Remaining work = 180 - 120 = 60

Remaining work done by (B + C) in = \(\frac{60}{5}\) = 12 min