Question

Tick (✓) the correct answer:
Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be full?
(a) 7 hrs 15 min
(b) 7 hrs 30 min
(c) 7 hrs 45 min
(d) 8 hrs

Answer 1

(b) 7 hours 30 minutes

$$\begin{gathered} \text{Part of the tank filled by the first pipe in one hour}=\frac{1}{10} \\ \text{Part of the tank filled by the second pipe in one hour}=\frac{1}{12} \\ \text{Part of the tank filled by the third pipe in one hour}=\frac{-1}{20} \\ \text{Part of the tank filled by three pipes in one hour}=\frac{1}{10}+\frac{1}{12}-\frac{1}{20}=\frac{2}{15} \\ \mathrm{Total}\mathrm{time}\mathrm{taken}\mathrm{to}\mathrm{fill}\mathrm{the}\mathrm{tank}=\frac{15}{2}\mathrm{hrs}=7\mathrm{hours}30\mathrm{minutes} \end{gathered}$$