Question

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

First tap's 1 hours work to fill $=\frac{1}{8}$

Second tap's 1 hours work to empty $=\frac{1}{16}$

Both's 1 hour fill the cistern

$=\frac{1}{8}-\frac{1}{16}=1$

$=\frac{2-1}{16}=\frac{1}{16}$

$\therefore$ The cistern will fill up in 16 hours