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?

Solution(By Examveda Team)

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