Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank will be filled?
1). 7 hrs
2). 8 hrs
3). 7 hrs. 30 min.
4). 8 hrs. 30 min.
Time taken by A , B and C to fill/empty the tank completely = 10 , 12 and 20 hours respectively
Hence part of tank filled by A, B and emptied by C in 1 hour = 1/10, 1/12 and 1/20 respectively
Part of tank filled by all 3 pipes in 1 min $(= \frac{1}{{10}} + \frac{1}{{12}}\; - \frac{1}{{20}})$
$(= \frac{6}{{60}}\; + \frac{5}{{60}}-\frac{3}{{60}})$
$(= \frac{8}{{60}})$
= 2/15
Hence it will take 15/2 hours ie 7 hours and 30 mins to completely fill the tank