Question

Tap A can fill a tank in 8 hours and tap B can empty the tank in $12$ hours. How long would it take to fill the empty tank if both of them are opened together?

Answer 1

Tap A fills on 8 hours $=1$ tank
tap A fills in 1 hour $=\frac{1}{8}$ tank
Tap B empties in 12 hours $=1$ tank
Tap B empties in 1 hour $=\frac{1}{12}$ tank
$\therefore$ Both taps will fill in 1 hour $=(\frac{1}{8}-\frac{1}{12})$ tank
$=\frac{3-2}{24}=\frac{1}{24}$
Hence, the tank will be filled completely in $24$ hours