Question

Tick (✓) the correct answer:
A tap can fill a cistern in 8 hours and another tap can empty the full cistern in 16 hours. If both the taps are open, the time taken to fill the cistern is
(a) $5\frac{1}{3}$ hours
(b) 10 hours
(c) 16 hours
(d) 20 hours

Answer 1

(c) 16 hours

$$\begin{gathered} \mathrm{A}\mathrm{tap}\mathrm{can}\mathrm{fill}\mathrm{a}\mathrm{cistern}\mathrm{in}8\mathrm{hours}. \\ \text{Part of cistern filled in one hour}=\frac{1}{8} \\ \mathrm{A}\mathrm{tap}\mathrm{can}\mathrm{empty}\mathrm{the}\mathrm{cistern}\mathrm{in}16\mathrm{hours}. \\ \mathrm{Part}\mathrm{of}\mathrm{cistern}\mathrm{emptied}\mathrm{in}\mathrm{one}\mathrm{hour}=-\frac{1}{16}(\mathrm{negative}\mathrm{sign}\mathrm{shows}\text{that}\mathrm{the}\mathrm{cistern}\mathrm{is}\mathrm{being}\mathrm{drained}) \\ \therefore \text{Part of cistern filled in one hour}=\frac{1}{8}-\frac{1}{16}=\frac{1}{16} \\ \mathrm{Time}\mathrm{required}\mathrm{to}\mathrm{fill}\mathrm{the}\mathrm{cistern}=16\mathrm{hours} \end{gathered}$$