Pipe A can fill a tank in 24 hours and pipe B in 32 hours. If both the pipes are opened in an empty tank at the same time, then the time taken to fill the tank is:

$13\frac{5}{7}$ hours

The correct answer is Option (3) → $13\frac{5}{7}$ hours **

Rate of pipe A = $\frac{1}{24}$

Rate of pipe B = $\frac{1}{32}$

Total rate = $\frac{1}{24} + \frac{1}{32}$

$= \frac{4}{96} + \frac{3}{96} = \frac{7}{96}$

Time taken = $\frac{96}{7}$ hours

The tank will be filled in $\frac{96}{7}$ hours.