Question

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 ______.

Options

• 5 hours

• 1 hour

• 6 hours

• none of these

Answer 1

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 6 hours.

Explanation:

Given,

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

So, one hour work of the pipe = `1/2`

Another pipe empties the full tank in 3 hours.

So, one hour work of other pipe = `-1/3`

When both pipes are opened together

= `2/1​ + (−1/13)`

= `1/2 - 1/3`

= `(1 xx 3)/(2 xx 3) - (1 xx 2)/(3 xx 2)`

= `3/2 - 2/6`

= `1/6`

Total time taken to fill the tank = `1/(1/6)` = 6 hours.