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?

The correct option is A

3 hrs 45 min

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

Part filled by one tap in 1 hour = $\frac{1}{6}$
Part filled by four taps in 1 hour = $(4\times \frac{1}{6})$ = $\frac{2}{3}$

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

$\frac{2}{3}$ of the tank is filled by four taps in 1 hour.
So, $\frac{1}{2}$ of the tank is filled in = $\frac{3}{2}\times \frac{1}{2}=\frac{3}{4}hours$

$\frac{3}{4}$ hours = $\frac{3}{4}\times 60=45min$

So, the total time taken = 3 hrs + 45 min = 3 hrs 45 min or 225 min