Question

Three taps can fill a tank .tap 1 can fill the tank in 30 minutes. tap b can fill the tank in 40 minutes and tank c can fill the tank in 60 minutes. if all three taps are open together how long will it take to fill the tank​

Answer 1

Answer:

Answer: 45 min

Explanation:

Given taps a and b can fill the tank in 30 and 40 minutes respectively. Therefore,

Part filled by tap a in 1 minute = 1/30

Part filled by tap b in 1 minute = 1/40

Part filled by tap c in 1 minute = 1/60

Net part filled by Pipes a, b, c in 1 minute = [1/30 +1/40 +1/60] = 540/720 = 3/4

i.e., the tank can be filled in 45 minutes.

Answer 2

$\begin{gathered}\Large{\textsf{\textbf{\underline{\underline{Given\::}}}}} \\ \end{gathered}$

A tap can fill a overhead water tank in 40 minute.

Another tap can fill it in 60 minute.

$\begin{gathered}\Large{\textsf{\textbf{\underline{\underline{To\:do\::}}}}} \\ \end{gathered}$

The time taken to fill the tank when the two taps are opened simultaneously.

$\begin{gathered}\Large{\textsf{\textbf{\underline{\underline{Solution\::}}}}} \\ \end{gathered}$

Let,

Tap A takes 40 minutes to fill the tank.

Tap B takes 60 minutes to fill the tank.

And,

Both tap A & B takes x minutes to fill the tank.

As per the statement,

✯ The equation becomes,

$\: \begin{gathered}\orange\bigstar\:{\Large\mid}\:\bf{\dfrac{1}{40}\:+\:\dfrac{1}{60}\:=\:\dfrac{1}{x}\:}\:{\Large\mid}\:\green\bigstar \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\tt{\dfrac{3\:+\:2}{120}\:=\:\dfrac{1}{x}\:} \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\tt{\dfrac{5}{120}\:=\:\dfrac{1}{x}\:} \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\tt{\dfrac{1}{x}\:=\:\dfrac{5}{120}\:} \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\tt{x\:=\:\dfrac{120}{5}\:} \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\bf\pink{x\:=\:24\: minutes} \\ \\ \end{gathered}$

∴ The time taken to fill the tank is 24 minutes, when the two taps are opened simultaneously.

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