An empty tank is filled by a pipe in 2 hours, whereas an another pipe empties the full tank in 3 hours. If the tank is empty and both the pipes are opened together the tank will be filled in:

1. 5 hours

2. 1 hour

3. 6 hours

4. none of these

6 hours

Reason

Given,

An empty tank is filled by a pipe in 2 hours.

So, one hour work of the pipe = $\dfrac{1}{2}$

Another pipe empties the full tank in 3 hours.

So, one hour work of other pipe = -$\dfrac{1}{3}$

When both pipes are opened together

$= \dfrac{1}{2} + \Big(-\dfrac{1}{3}\Big)\\[1em] = \dfrac{1}{2} - \dfrac{1}{3}\\[1em] = \dfrac{1 \times 3}{2 \times 3} - \dfrac{1 \times 2}{3 \times 2}\\[1em] = \dfrac{3}{6} - \dfrac{2}{6}\\[1em] = \dfrac{1}{6}$

Total time taken to fill the tank = $\dfrac{1}{\dfrac{1}{6}}$ = 6 hours.

Hence, option 3 is the correct option.