A CISTERN HAS 2 TAPS ONE AT THE TOP AND OTHER AT THE BOTTOM. THE TOP TAP FILLS THE CISTERN IN ONE HOUR AND THE BOTTOM TAP EMPTIES THE CISTERN IN 1.5HOURS .IF BOTH TAPS KEPT OPEN AT THE SAME TIME, IN HOW MANY HOURS THE CISTERN WILL BE FILLED IN FULLY?

Let the volume of the cistern be V

Hence, the rate by which the top tap fills the cistern is V/1 

and the rate by which the bottom tap empties the cistern is V/1.5

 

Hence, if both the taps are open at the same time, let the time taken for the cistern to get filled be t hours

(V/1 - V/1.5) * t =V

t = 1.5/0.5 = 3 hours