Question

sum of the digits of a two digit number is 13 The number got by interchanging the digits is 27 more than the orginal number.find the number.​

Answer 1

Given:

• Digits of two digit number add up to 13
• The number increases by 27 when digits are Interchanged

To Find:

• The original number

Solution:

Let the tens digit of the original n. = x

Let the ones digit of the original n. = y

The original number

⟹ 10x + y

The number when Interchanged :

⟹ 10y + x

According to the question:

New number = Original number + 27

⟹ ( 10y + x ) = ( 10x + y ) + 27

⟹ ( 10y + x ) - ( 10x + y ) = 27

⟹ 10y + x - 10x - y = 27

⟹ 9y - 9x = 27

⟹ 9 ( y - x ) = 27

⟹ y - x = 27/9

⟹ y - x = 3

⟹ y = x + 3

y should be greater than x

Let x = 1

Then y = x + 3 = 4

One of the possible number is 14

Answer 2

${\tt{\green{\underline{\underline{\huge{Answer:-}}}}}}$

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$\LARGE{\bf{\underline{\underline\color{red}{GIVEN:-}}}}$

$\sf\color{blue}{→Let\: the\: <strong>Tens</strong><strong> </strong>\: digit \:be=\: x}$

$\sf\color{blue}{→Let\: the\: <strong>Once</strong> \: digit \:be=\: y}$

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$\mathrm{\boxed{\boxed{\pink{→ The\: orginal \: number }}}}$

$\sf\color{red}{→\:10x\:+\:y}$

$\mathrm{\boxed{\boxed{\pink{→ The\: interchanged \: number }}}}$

$\sf\color{red}{→\:10y\:+\:x}$

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

$\mathrm{\boxed{\boxed{\pink{→ New \: number =\: Orginal \: number \:+ \: 27 }}}}$

$\sf\color{red}{→(10y+x)\:= \: (10x+y)\: +27}$

→(10y+x) -(10x+y ) = 27

→10y +x -10x -y = 27

→9y - 9x = 27

→9 ( y-x ) = 27

→y - x = 27/9

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{ →y\: - x \: = \: 3}} }\\ \\\end{gathered}\end{gathered}$

$\mathrm{\boxed{\boxed{\red{→ y\: = \: x \: + \: 3 }}}}$

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Y should be greater then x

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So ,

$\mathrm{\boxed{\boxed{\blue{→ X \: = 1}}}}$

$\mathrm{\boxed{\boxed{\blue{→ Y \: = \: x+3 \: = \: 4}}}}$

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$\sf\color{red}{→So, \: The \: number \: = \: 14}$

${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$