Question 108

# Nitin installed an overhead tank on the roof of his newly constructed house. Three taps are connected to the tank: 2 taps A and B to fill the tank and one tap C to empty it. Tap A alone can fill the tank in 12 hours, while tap B alone takes one and a half times more time than tap A to fill the tank completely. Tap C alone can empty a completely filled tank in 36 hours. Yesterday, to fill the tank, Nitin first opened tap A, and then after 2 hours opened tap B also. However after 6 hours he realised that tap C was open fi-om the very beginning. He quickly closes tap C. What will be the total time required to fill the tank?

Solution

Tap A alone can fill the tank in 12 hours
Tap B alone can fill the tank in 12*1.5 = 18 hours
Tap C alone can empty the tank in 36 hours
Let the total volume of the tank be 36 units
A fills 3 units, B fills 2 units and C empties 1 units in an hour.
Let the total time taken be 't'
t(3) + (t-2)2 - 6(1) = 36
5t = 46
t = 9.2 hrs = 9 hours 12 minutes

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