A tap can fill a tank in 12 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A tap can fill the tank in 12 hours
One hour work of one tap = 1/12
⇒ One hour work of 4 taps = 4/12 = 1/3

4 taps 1/3 part can fill the tank in 1 hour
4 taps 1 part can fill the tank in 1× 3 hours
4 taps 1/2 part can fill the tank in (1× 3)/2 hours
= 3/2 = 1.5 hours

⇒ Total time to fill the tank = 6 hours to first half + 1.5 hour to second half
∴ The required result will be 7.5 hours.