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Two pipes can fill a tank in 30 minutes and 60 minutes respectively. Another pipe at the bottom will empty it in 120 minutes. If all the pipes are open, in what time will the tank get filled?
$$ work done = efficiency \times time $$
work done = LCM( 30 , 60 , 120 ) = 120
efficiency of pipe P1 = $$ \frac{120}{30} = 4 $$
efficiency of pipe P2 = $$ \frac{120}{60} = 2 $$
efficiency of pipe P3 = $$ \frac{120}{120} = 1 $$
If all the pipes are open, in what time will the tank get filled $$ time = \frac{120}{5} = 24 minutes $$
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