Question

Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened together?

Answer 1

$$\begin{gathered} \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{tap}\mathrm{A}\mathrm{to}\mathrm{fill}\text{the}\mathrm{tank}=6\mathrm{hours} \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{tap}\mathrm{B}\mathrm{to}\mathrm{fill}\text{the}\mathrm{tank}=8\mathrm{hours} \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{tap}\mathrm{C}\mathrm{to}\mathrm{fill}\text{the}\mathrm{tank}=12\mathrm{hours} \\ \mathrm{A}\mathrm{fills}\frac{1}{6}\mathrm{of}\mathrm{the}\mathrm{tank}\text{in one hour.} \\ \mathrm{B}\mathrm{fills}\frac{1}{8}\mathrm{of}\mathrm{the}\mathrm{tank}\text{in one hour.} \\ \mathrm{C}\mathrm{fills}\frac{1}{12}\mathrm{of}\mathrm{the}\mathrm{tank}\text{in one hour.} \\ \text{Part of the tank filled in one hour using all the three pipes}=\frac{1}{6}+\frac{1}{8}+\frac{1}{12}=\frac{4+3+2}{24}=\frac{9}{24} \\ \text{Time taken by A, B and C together to fill the tank}=\frac{24}{9}=\frac{8}{3}=2\frac{2}{3}\mathrm{hours} \end{gathered}$$