Question

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

Answer 1

Hint: The given question is an example of word problem which is majorly based on the concept or work and time and we need to solve this. It involves the tank filling work with two pipes that obviously takes different time to fill and hence according to the given condition we need to find the total time needed to fill the tank.

Complete step-by-step solution:
According to the given question, we are given that tank filled by pipe A in one minute is $\dfrac{1}{15}$
And a tank filled by pipe B in one minute is $\dfrac{1}{20}$ .
Now, we are given that till 4 minutes both pipes fill the tank, therefore tank filled in 4 minutes using both the pipes is
$\begin{align}
  & 4\left( \dfrac{1}{15}+\dfrac{1}{20} \right) \\
 & \Rightarrow \dfrac{4}{5}\left( \dfrac{7}{12} \right) \\
 & \Rightarrow \dfrac{7}{15} \\
\end{align}$
Now, the tank unfilled is $1-\dfrac{7}{15}=\dfrac{8}{15}$
Now, the pipe B has to fill the remaining tank $\dfrac{8}{15}$ . Tank filled in one minute by pipe B is $\dfrac{1}{20}$.
Now, the remaining tank will be filled in $\dfrac{\dfrac{8}{15}}{\dfrac{1}{20}}\Rightarrow \dfrac{32}{3}$ .
Now, simplifying this to get time in minutes and seconds we get, $10\dfrac{2}{3}$which is 10minutes and 40seconds.
Therefore, the total time taken to fill the tank by both the pipes is 14minutes 40 seconds.

Note: In these types of questions all we need to do is do step by step calculations and write the values accordingly as per each statement and then proceed towards the solution in order to avoid any kind of mistake and so that all conditions are fully considered while solving.