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