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?

Answer: Option B

Time taken by one tap to fill half of the the tank = 3 hours
Part filled by the four taps in 1 hour
$$\begin{array}{rl}& =4\times \frac{1}{6}=\frac{2}{3}\\ & \text{Remaining}\text{part}=1-\frac{1}{2}=\frac{1}{2}\\ & \therefore \frac{2}{3}:\frac{1}{2}::1:x\\ & \Rightarrow x=\frac{1}{2}\times 1\times \frac{3}{2}\\ & =\frac{3}{4}hrs.i.e.,45\mathrm{mins}.\\ & \text{So,}\text{total}\text{time}\text{taken}=3hrs.45mins.\end{array}$$