A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled completely?

Question: A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled completely?

Solution:
A’s 1 hour’s work = 1/12
B’s 1 hour’s work = 1/16
C’s 1 hour’s work = 1/8

Therefore, (A + B + C)’s 1 hours net work= (1/12) + (1/16) - (1/8)
= (4 + 3 - 6)/48
= 1/48

So, time taken by (A + B + C) to fill the cistern = 48 hours.