Question

When 5 is added to one-fifth of a number , the sum is equal to 4 less than one-fourth of that number. Find the number .​

Answer 1

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

• When 5 is added to one-fifth of a number , the sum is equal to 4 less than one-fourth of that number. Find the number .

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

$\red{\boxed{ \sf \blue{ Let \:the\: Number\: be\: x }}}$

• One-fifth of x = $\sf\green{ \frac{1}{5} x \: = \: \frac{x}{5} }$
• One-fifth of x increased by 5 = $\sf\green{ \frac{x}{5} \: + \: 5 }$
• One-fourth of x = $\sf\green{\frac{1}{4} x \: = \: \frac{x}{4} }$
• 4 less than one-fourth of x = $\sf\green{ \frac{x}{4} \: - \: 4 }$

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

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{ \: \: \: \: \: \: \: According\: \: to \: \:the\: \: Question : \: \: \: \: }} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \frac{x}{5} \: + \: 5 \: = \: \frac{x}{4} \: - \: 4 }} }\\ \end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{x}{5} \: + \: 5 \: = \: \frac{x}{4} \: - \: 4 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{x}{5} \: - \: \frac{x}{4} \: = \: ( - 4 \: - 5) }}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ \frac{4x \: - \: 5x}{20} \: = \: - 9 }}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ \frac{-x}{20} \: = \: - 9 }}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ -x \: = \: - 9 \: \times \: 20}}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ -x \: = \: - 180}}$

$\qquad \quad {:}\longrightarrow\sf{\sf{ \cancel{-}x \: = \: \cancel{ - }180}}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 180 }}}$

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

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{x}{5} \: + \: 5 \: = \: \frac{x}{4} \: - \: 4 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{180}{5} \: + \: 5 \: = \: \frac{180}{4} \: - \: 4 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 36 \: + \: 5 \: = \: 45 \: - \: 4 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{41 \: = \: 41 }}}$

$\quad {:} \longrightarrow \sf{\sf\blue{Hence \: Verified }}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ x \: = \underline {\underline{180}}}\\\end{gathered}\end{gathered}$

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Answer 2

When 5 is added to one-fifth of a number , the sum is equal to 4 less than one-fourth of that number. Find the number .

\begin{gathered}\\ \\ \\ \end{gathered}

\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}

✠Given:−

\red{\boxed{ \sf \blue{ Let \:the\: Number\: be\: x }}}

LettheNumberbex

One-fifth of x = \begin{gathered}\sf\green{ \frac{1}{5} x \: = \: \frac{x}{5} }\\ \\\end{gathered}

5

1

x=

5

x

One-fifth of x increased by 5 = \begin{gathered}\sf\green{ \frac{x}{5} \: + \: 5 }\\ \\\end{gathered}

5

x

+5

One-fourth of x = \begin{gathered}\sf\green{\frac{1}{4} x \: = \: \frac{x}{4} }\\ \\\end{gathered}

4

1

x=

4

x

4 less than one-fourth of x = \begin{gathered}\sf\green{ \frac{x}{4} \: - \: 4 }\\ \\\end{gathered}

4

x

−4

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

✠Solution:−

\begin{gathered}\begin{gathered}\begin{gathered}\underline{\boldsymbol{ \: \: \: \: \: \: \: According\: \: to \: \:the\: \: Question : \: \: \: \: }} \\\end{gathered}\end{gathered} \end{gathered}

AccordingtotheQuestion:

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \frac{x}{5} \: + \: 5 \: = \: \frac{x}{4} \: - \: 4 }} }\\ \end{gathered}\end{gathered}\end{gathered}\end{gathered}

:⟹

5

x

+5=

4

x

−4

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{x}{5} \: + \: 5 \: = \: \frac{x}{4} \: - \: 4 }}\\ \\\end{gathered}

:⟶

5

x

+5=

4

x

−4

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{x}{5} \: - \: \frac{x}{4} \: = \: ( - 4 \: - 5) }}\\ \\\end{gathered}

:⟶

5

x

−

4

x

=(−4−5)

\begin{gathered}\qquad \quad {:}\longrightarrow\sf{\sf{ \frac{4x \: - \: 5x}{20} \: = \: - 9 }}\\ \\\end{gathered}

:⟶

20

4x−5x

=−9

\begin{gathered}\qquad \quad {:}\longrightarrow\sf{\sf{ \frac{-x}{20} \: = \: - 9 }}\\ \\\end{gathered}

:⟶

20

−x

=−9

\begin{gathered}\qquad \quad {:}\longrightarrow\sf{\sf{ -x \: = \: - 9 \: \times \: 20}}\\ \\\end{gathered}

:⟶−x=−9×20

\begin{gathered}\qquad \quad {:}\longrightarrow\sf{\sf{ -x \: = \: - 180}}\\ \\\end{gathered}

:⟶−x=−180

\begin{gathered}\qquad \quad {:}\longrightarrow\sf{\sf{ \cancel{-}x \: = \: \cancel{ - }180}}\\ \\\end{gathered}

:⟶

−

x=

−

180

\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 180 }}}:⟶

x=180

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\large\underline{ \underline{ \sf \maltese{ \: Verification:- }}}

✠Verification:−

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{x}{5} \: + \: 5 \: = \: \frac{x}{4} \: - \: 4 }}\\ \\\end{gathered}

:⟶

5

x

+5=

4

x

−4

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{180}{5} \: + \: 5 \: = \: \frac{180}{4} \: - \: 4 }}\\ \\\end{gathered}

:⟶

5

180

+5=

4

180

−4

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{ 36 \: + \: 5 \: = \: 45 \: - \: 4 }}\\ \\\end{gathered}

:⟶36+5=45−4

\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{41 \: = \: 41 }}}:⟶

41=41

\begin{gathered} \quad {:} \longrightarrow \sf{\sf\blue{Hence \: Verified }}\\ \\\end{gathered}

:⟶HenceVerified

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\begin{gathered}\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ x \: = \underline {\underline{180}}}\\\end{gathered}\end{gathered} \end{gathered}

∴x=

180

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