Question

A number is first increased by 25% and then decreased by 25%. find the net increase or decrease percentage​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• A number is first increased by 25% and then decreased by 25%. Find the net increase or decrease ppercentage.

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\boxed{ \sf \orange{Let \:the \:number\: be \:100 }}$

$\sf\green{ Number \:after\: an \:increase \:of\: 25\%}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 100 + 25 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \: 125 }}}$

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$\sf\green{ Decrease \:in\: the \:new \:number \:= 25\% \:of \:125 }$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{25}{100} \: \times \: 100 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \: 31.25 }}}$

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$\sf\green{ Final \:Number \:= 125 - 31.25 }$

$\qquad\quad {:} \longrightarrow \underline \blue{\boxed{\sf{ \: 93.75}}}$

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$\sf\green{ Net \:decrease \:= 100 - 93.75 }$

$\qquad\quad {:} \longrightarrow \underline \blue{\boxed{\sf{ \: 6.25}}}$

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Thus, net percentage decrease

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{6.25}{1\cancel{0}\cancel{0}} \: \times \: 1 \cancel{0}\cancel{0} }}$

$\qquad\quad {:} \longrightarrow \underline \purple{\boxed{\sf{ \: 6.25\%}}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Decrease \: Percentage= \underline {\underline{ 6.25\% }}}\\\end{gathered}\end{gathered}$

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Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

A number is first increased by 25% and then decreased by 25%. Find the net increase or decrease ppercentage.

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\boxed{ \sf \orange{Let \:the \:number\: be \:100 }}$

$\sf\green{ Number \:after\: an \:increase \:of\: 25\%}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 100 + 25 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \: 125 }}}$

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$\sf\green{ Decrease \:in\: the \:new \:number \:= 25\% \:of \:125 }$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{25}{100} \: \times \: 100 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \: 31.25 }}}$

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$\sf\green{ Final \:Number \:= 125 - 31.25 }$

$\qquad\quad {:} \longrightarrow \underline \blue{\boxed{\sf{ \: 93.75}}}$

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$\sf\green{ Net \:decrease \:= 100 - 93.75 }$

$\qquad\quad {:} \longrightarrow \underline \blue{\boxed{\sf{ \: 6.25}}}$

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Thus, net percentage decrease

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{6.25}{1\cancel{0}\cancel{0}} \: \times \: 1 \cancel{0}\cancel{0} }}$

$\qquad\quad {:} \longrightarrow \underline \purple{\boxed{\sf{ \: 6.25\%}}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Decrease \: Percentage= \underline {\underline{ 6.25\% }}}\\\end{gathered}\end{gathered}$

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