Question

13. A tap can fill a tank in 4 hours. But one day it
took 7 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 be
empty?​

Answer 1

Answer:

$\sf{Time\: taken\: by\: the\: outlet\: pipe\: to \:empty\: the\: tank =9\dfrac{1}{3} \:hours}$

Given:

• A tap can fill a tank in 4 hours.
• But one day, it took 7 hours to fill the tanks as the outlet pipe was open.

To Find:

• If the tap is closed and the outlet pipe is left open, how much time will it take for the tank to be empty?

Process:

To find the time taken by the outlet pipe to empty the tank we first have to find the work done by the tap in one hour and work done by the tap and outlet pipe together in one hour. After, that we will subtract work done by the tap and outlet pipe together in one hour from work done by the tap in one hour. As the result we will get the work done by the outlet pipe in one hour. Then we can get time taken by the outlet pipe to empty the tank.

Solution:

Time taken for the tap to fill the tank = 4 hours

Work done by the tap in one hour = 1/4

Time taken by the tap and the outlet pipe together to fill the tank = 7 hours

Work done by the tap and the outlet pipe together in one hour = 1/7

Work done by the outlet pipe in 1 hour = 1/4 - 1/7

$=\sf{\dfrac{7-4}{28}= \dfrac{3}{28}}$

Time taken by the outlet pipe to empty the tank = 28/3 hours

$\sf{=9\dfrac{1}{3} \:hours}$