Question

There are two pipes, an inlet pipe , which completely fills a tank at \[6\] \[litre/\min \] and an outlet pipe which empties the tank at \[4\] \[litre/\min \] .The pipe function alternately for \[1\] minute and the inlet pipe is the first to function. Considering the capacity of the tank as \[50\] \[litres\] , how much time will it take to completely fill the tank?

Answer 1

Hint: In this question, we were given a tank which contains two pipes of which one is inlet and other is outlet pipe. The pipes function alternatively for a minute each and their rates at which inlet and outlet of water is done was given. The capacity of the tank was given, we must find the total time to completely fill the tank. Now using the rates given we find the net rate of inlet of water and compute the solution.

Complete step-by-step answer:
According to the question, the pipes functions alternately each a for a minute and the inlet pipe is first to function, so we write
Initially the tank is empty and for the first minute the inlet pipe is opened which has the rate of filling the tank as \[6\] \[litre/\min \].Therefore it means it fills \[6\] litres per minute. Now the tank contains \[6\]litres of water .In the next minute as the pipes function alternately outlet pipe is opened ,it has a rate of emptying tank as \[4\] \[litre/\min \].Therefore it means it empties \[4\] litres per minute .Now as the tank already contains \[6\]litres, outlet pipe releases \[4\]litres of it and the remaining quantity of water in tank will be \[2\]litres in total time of two minutes.
Therefore we write the net rate of water inflow \[R = \dfrac{{2litres}}{{2\min }} = 1litre/\min \] .
Now a total volume 50 litres should be filled so we write,
\[R = \dfrac{{volume}}{{time}}\]
\[R = 1 = \dfrac{{50}}{{time}}\]
\[ \Rightarrow time = 50\min \]
Therefore, the total time required to fill the tank will be \[50\] minutes.
So, the correct answer is “50 Mins”.

Note: While solving this question, all the main terms such as inlets, outlets etc. should be known. Inlet and outlet features allow water to flow into and out of features and also limit the rate at which water flows along and out of the system. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.