Question

The sum of two digits of a number is 9. If 9 is subtracted from the number, then the digits are reversed. The number is:
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please tell me this,, ​

Answer 1

❍ Let's say, the unit place digit be x and ten's place digit be y respectively.

➠ The number is (10y + x).

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$\underline{\bigstar\:\boldsymbol{According \;to \;the\: given \;Question\; :}}$

• The sum of two digits of a number is 9.

Therefore,

➠ x + y = 9

➠ x = 9 - y ⠀⠀⠀⠀⠀⠀⠀⠀⠀—eq( I ).

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Also,

⠀⠀⠀⠀

• If 9 is subtracted from the number, then the digits are reversed.

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Therefore,

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$:\implies\sf 10y + x - 9 = 10x + y \\\\\\:\implies\sf 10y + x - 10x - y = 9 \\\\\\:\implies\sf 9y - 9x = 9\\\\\ \\ \footnotesize \: \: \: \: \: \: \: \: \: \: \dag \sf \: \: Taking\:common\:9 \\\\\\:\implies\sf 9(y - x) = 9\\\\\\:\implies\sf y - x = \cancel\dfrac{9}{9}\\\\\\:\implies\sf y - x = 1$

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F R O M EQn I :

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$:\implies\sf y -x = 1 \\\\\\:\implies\sf y - 9 - y = 1\\\\\\:\implies\sf 2y = 10\\\\\\:\implies\sf y = \cancel\dfrac{10}{2}\\\\\\:\implies\underline{\boxed{\frak{\pmb{\pink{y = 5}}}}}\;\bigstar$

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And,

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$:\implies\sf x + y = 9\\\\\\:\implies\sf x + 5 = 9\\\\\\:\implies\sf x = 9 - 5 \\\\\\:\implies\underline{\boxed{\frak{\pmb{\pink{x = 4}}}}}\;\bigstar$

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$\therefore{\underline{\textsf{Hence, \;the\; required\; number\;is\:\textbf{54}.}}}$

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V E R I F I C A T I O N :

• It is given as, the sum of both two digits number is 9. So, let's verify the digits : ⠀⠀

Therefore,

$\dashrightarrow\sf x + y = 9 \\\\\\\dashrightarrow\sf 5 + 4 = 9\\\\\\\dashrightarrow\underline{\boxed{\frak{\pmb{9 = 9}}}}$

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$\qquad\qquad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$

Answer 2

Question:-

• The sum of two digits of a number is 9. If 9 is subtracted from the number, then the digits are reversed. The number is

To Find:-

• Find the number.

Solution:-

• Let the unit place digit be x and the ten's place digit be y.

Given ,

• x + y = 9 . . . . ( 1 )

The two numbers are:-

• 10y + x and 10x + y

According to the question:-

$\longrightarrow\sf \: 10y + x - 9 = 10x + y$

$\longrightarrow\sf \: 10y - y = 10x - x + 9$

$\longrightarrow\sf \: 9y = 9x + 9$

$\longrightarrow\sf \: 9y - 9x = 9$

$\longrightarrow\sf \: 9( y - x ) = 9$

$\longrightarrow\sf \: y - x = \cancel\dfrac { 9 } { 9 }$

$\longrightarrow\sf \: y - x = 1$ . . . . ( 2 )

Add equation ( 1 ) and ( 2 ):-

$\longrightarrow\sf \: y - x + x + y = 9 + 1$

$\longrightarrow\sf \: 2y = 10$

$\longrightarrow\sf \: y = \cancel\dfrac { 10 } { 2 }$

$\longrightarrow\sf \: y = 5$

Now ,

Substitute ' y ' value in equation

( 1 ):-

$\longrightarrow\sf \: x + y = 9$

$\longrightarrow\sf \: x + 5 = 9$

$\longrightarrow\sf \: x = 9 - 5$

$\longrightarrow\sf \: x = 4$

Hence ,

• The number is 54