Question

Q.3 Two pipes running together can fill a cistern in 24 hours. If one pipe takes
2 hours more than the other to fill the cistern, find the time in which each pipe
would fill the cistern.​

Answer 1

Given:

• Two pipes running together can fill a cistern in 24 hours

• one pipe takes2 hours more than the other to fill the cistern

To Find:

• find the time in which each pipe would fill the cistern.

$\sf{ \large {\underline{ \underline \orange{ \maltese \: understanding \: the \: question : }}}}$

• ➢ here we know that the time taken to fill the cistern is 24 hours and it's given that a pipe takes two hours more to fill compared to the second pipe.!

• ➢ so, now let the time taken by faster pipe be x mins

• ➢ and the time taken by the slower pipe be (x+2) mins

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Solution:

$\tt: \longrightarrow \: the \: portion \: of \: water \: filled \: pipe \: 1 \: in \: 1hr = \frac{1}{x} \: \: \: \: \: \: \: \: \\ \\ \\ \tt: \longrightarrow the \: portion \: of \: water \: filled \: by \: pipe1 \: in \: 24hr = \frac{24}{1x} \\ \\ \\ \tt: \longrightarrow the \: portion \: of \: water \: filled \: by \: pipe2 = \frac{24}{1(x + 2)} \: \: \: \: \\ \\ \\ \tt: \longrightarrow a \: cistren \: is \: filled \: in \: 24hrs \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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$: \implies \sf \: \frac{24}{1x} + \frac{24}{1(x + 2)} = 1 \\ \\ \\ \\ : \implies \sf \frac{1}{x} + \frac{1}{x + 2} = \frac{1}{24} \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: x + x + 2 = 24 \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: 2x + 2 = 24 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf2x = 22 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: x = \cancel \frac{22}{2} \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: x = 11hrs \bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

➵ now the time taken for the first pipe:

$\rm \pink {\longmapsto 11hrs(x)}$

➵ the time taken by the second pipe:

$\rm \pink {\longmapsto \: 13hrs(x + 2)}$

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Answer 2

Given:

Two pipes running together can fill a cistern in 24 hours

one pipe takes2 hours more than the other to fill the cistern

To Find:

find the time in which each pipe would fill the cistern.

$\sf{ \large {\underline{ \underline \orange{ \maltese \: understanding \: the \: question : }}}}$

➢ here we know that the time taken to fill the cistern is 24 hours and it's given that a pipe takes two hours more to fill compared to the second pipe.!

➢ so, now let the time taken by faster pipe be x mins

➢ and the time taken by the slower pipe be (x+2) mins

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Solution:

$\begin{lgathered}\tt: \longrightarrow \: the \: portion \: of \: water \: filled \: pipe \: 1 \: in \: 1hr = \frac{1}{x} \: \: \: \: \: \: \: \: \\ \\ \\ \tt: \longrightarrow the \: portion \: of \: water \: filled \: by \: pipe1 \: in \: 24hr = \frac{24}{1x} \\ \\ \\ \tt: \longrightarrow the \: portion \: of \: water \: filled \: by \: pipe2 = \frac{24}{1(x + 2)} \: \: \: \: \\ \\ \\ \tt: \longrightarrow a \: cistren \: is \: filled \: in \: 24hrs \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\end{lgathered}$

$\begin{lgathered}: \implies \sf \: \frac{24}{1x} + \frac{24}{1(x + 2)} = 1 \\ \\ \\ \\ : \implies \sf \frac{1}{x} + \frac{1}{x + 2} = \frac{1}{24} \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: x + x + 2 = 24 \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: 2x + 2 = 24 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf2x = 22 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: x = \cancel \frac{22}{2} \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \\ \\ \\ \\ : \implies \sf \: x = 11hrs. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\end{lgathered}$

➵ now the time taken for the first pipe:

$\rm \pink {\longmapsto 11hrs(x)}$

➵ the time taken by the second pipe:

$\rm \pink {\longmapsto \: 13hrs(x + 2)}$

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