A tap can fill a tank in 4 hours. After half the tank is filled, five more similar taps are opened. What is the total time taken to fill the tank completely ?

Time taken by tap to fill the half of the part $=\frac{4}{2}hrs\Rightarrow 2hours$

6 taps fill the tank in 1 hour = $6\times \frac{1}{4}=\frac{3}{2}$

$\begin{array}{l}\text{Remaining}=\frac{1}{2} fill in\\ 1 hr\to \frac{3}{2} part\\ x hr \to \frac{1}{2 } part\\ x=\frac{1}{2}\times 1\times \frac{2}{3}=\frac{1}{3}hr=20 min\\ \therefore totaltime\Rightarrow 2hr+20\min \left(or\right)\\ 6taps\Rightarrow \text{Remaining\hspace{0.17em}\hspace{0.17em}}half\text{\hspace{0.17em}\hspace{0.17em}tank\hspace{0.17em}\hspace{0.17em}}willtake2hrs\\ =\frac{120}{6}=20\\ \Rightarrow 20\min \Rightarrow total=2hrs20\min \end{array}$