A tap can fill a tank in 7 hours. After half the tank is filled four more similar taps are opened. What is the total time taken to fill the tank completely?

Time taken to fill the tank by the tap = 7 hours 

So, part of the tank filled by a tap in

1 hour $=\frac{1}{7}$

Part of the tank filled by 5 taps in 1 hour

$=\frac{5}{7}$

$\therefore$ Time taken to fill the tank by 5 taps $=\frac{7}{5}\text{ hours }$

$\Rightarrow$time taken to fill the half tank by 5 taps $=\frac{1}{2}\times \frac{7}{5}\text{ hours }$

Time taken to fill the half tank by one tap $=3\frac{1}{2}$hours.

So, total time to fill the full tank

$=3\frac{1}{2}\text{ hours }+\frac{1}{2}\times \frac{7}{5}\text{ hours }$

$=\left(\frac{7}{2}+\frac{7}{10}\right)\text{ hours }=\frac{42}{10}\text{ hours }=4.2\text{ hours }$

$\therefore$ Option (a) is the correct answer.