A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Time taken by one tap to fill half of the tank = 3 hrs.

  Part filled by the four taps in 1 hour =4*1/6 =2/3

Remaining part = $1-\frac{1}{2}=\frac{1}{2}$

$\frac{2}{3}:\frac{1}{2}::1:x$

=> x =  $\frac{1}{2}*1*\frac{3}{2}=\frac{3}{4}$

So, total time taken = 3 hrs. 45 mins.