Time required by two pipes A and B working separately to fill a tank is 36 seconds and 45 seconds respectively. Another pipe C can empty the tank in 30 seconds. Initially, A and Bare opened and after 7 seconds, C is also opened. In how much more time the tank would be completely filled?
Solution
We will assume the capacity of the tank to be 180 litres i.e. LCM of 36, 45 and 30.
This gives the efficiency of Pipe A = 180/36 = 5 l/sec,
efficiency of Pipe B = 180/45 = 4 l/sec and efficiency of Pipe C = 180/30 = 6 l/sec.
For the first 7 seconds, Pipe A and Pipe B were opened which means that they filled 7*(5+4) = 63 litres.
Remaining quantity to be filled = 180 - 63 = 117 and time taken will be $$\frac{117}{5+4-6}=39\ \sec onds$$.
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