
Cistern Problem
A cistern can be filled by taps a,b in 12 hrs and 6 hrs respectively.The full cistern can be emptied by a third tap c in 8 hrs.If all the taps be turned on at the same time, in how much time will the empty cistern be filled completly?
(a)48 hrs
(b)40 hrs
(c)36 hrs
(d)24 hrs

if 24 L tank
Lets us choose to work with a 24 L tank, as the size does not matter.
I choose 24 as 24 = LCF(6,8,12)
tap A adds at 2L per hour
tap B adds at 4L per hour
tap C empties at 3 L per hour.
net effect is 2 + 4  3 = add 3 L per hour
hence it will take 24 / 3 = 8 hours
cheers