Question

A tank of capacity 25 litres has an inlet and an outlet tap. If both are opened simultaneously, the tank is filled in 5 minutes. But if the outlet flow rate is doubled and both the taps are opened, the tank never gets filled up. Which of the following can be outlet flow rate in litre/min?
a.)2
b.)6
c.)4
d.)3

Answer 1

\(\large \begin{align} \color{black}{
\normalsize \text{let A(inlet) takes x min and B(outlet) takes y min to fill/emplty the tank } \hspace{.33em}\\~\\
A \rightarrow x~min \hspace{.33em}\\~\\
B \rightarrow y~min \hspace{.33em}\\~\\
A+B \rightarrow 5~min \hspace{.33em}\\~\\
total~~work=25 litres~~\hspace{.33em}\\~\\
A = \dfrac{25}{x}~L/min\hspace{.33em}\\~\\
B = -\dfrac{25}{y}~L/min \hspace{.33em}\\~\\
A+B =\dfrac{25}{ 5}=5~L/min \hspace{.33em}\\~\\
\dfrac{25}{x}-\dfrac{25}{y}=5 \hspace{.33em}\\~\\
\dfrac{1}{x}-\dfrac{1}{y}=\dfrac{1}{5} \hspace{.33em}\\~\\
}\end{align}\)

how can i proceed from here

Answer 2

that means \(i - o = 5 ~L/min\)
where \(i = \) input flow rate
\(o\) = output flow rate

Answer 3

then we have \((i-o)t = 25\)
\[t = \dfrac{25}{i-o}\]

double the actual output flow rate :
\[t = \dfrac{25}{i-2o}\]

replace \(i\) by \(5+o\) :
\[t = \dfrac{25}{5+o-2o}\]
\[t = \dfrac{25}{5-o}\]

Answer 4

Clearly \(t\to \infty\) as \(o\to 5\)
so the time is undefined for \(o \ge 5\)

Answer 5

ok it was \(\large 6\) thnks