Question

5. A tank can be filled by a tap in 5 hours. But
one day it took 6 hours to fill the tank as the
outlet pipe was open. If the tap is closed and
the outlet pipe is left open, how long will it
take for the tank to get empty?​

Answer 1

Answer:

30 hrs

Step-by-step explanation:

Let the inflow rate be x m^3/hr

Let the volume of the tank be V m^3

Therefore

$x = \frac{v}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (1)$

Now, let's assume that the outflow rate as y m^3/hr

Hence total flow = x-y

Therefore

$(x - y) \times 6 = v$

Using eqn (1) in the above equation, we have

$( \frac{v}{5} - y) \times 6 = v$

$y = \frac{v}{30} {m}^{3} per \: hr$

Hence, When only outlet is open, the tank will become empty in

$\frac{v}{y} \: \: hrs$

$= \frac{v}{ \frac{v}{30} } = 30hrs$