Question

Ques- The sum of a two digit no. and then number
obtained by reversing the order of digit is 105 . when 9 is subtracted from the no. the digit interchange their places. find the no.
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Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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As your given question doesn't give any natural number hence,

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Correct question :

The sum of a two digit no. and then number

The sum of a two digit no. and then numberobtained by reversing the order of digit is 165 . when 9 is subtracted from the no. the digit interchange their places. find the no.

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$\green{\underline \bold{Given :}}$

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• Sum of a two digit no. and then number obtained by reversing the order of digit is 165 .

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• When 9 is subtracted from the no. the digit interchange their places.

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$\red{\underline \bold{To \: Find:}}$

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• The original number

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the tens digit be 'x'

Let the ones digit be 'y'

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$\underline{\bold{\texttt{Original Number :}}}$

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$\purple\longrightarrow$ $\sf 10x + y$

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$\underline{\bold{\texttt{Reversed Number :}}}$

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$\purple\longrightarrow$ $\sf 10y + x$

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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Sum of original number and reversed number is 165

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$\sf \longmapsto 10x + y + 10y + x = 165$

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$\sf \longmapsto 11x + 11y = 165$

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$\underline{\bold{\texttt{Dividing the above equation by 11 }}}$

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$\sf \longmapsto x + y = 15$ ------(1)

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Also,

When 9 is subtracted from the no. the digit interchange their places.

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$\sf \longmapsto 10x + y - 9 = 10y + x$

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$\sf \longmapsto 9x - 9y = 9$

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$\underline{\bold{\texttt{Dividing the above equation by 9 }}}$

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$\sf \longmapsto x - y = 1$ -------(2)

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$\underline{\bold{\texttt{Adding (1) \& (2)}}}$

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$\sf \longmapsto x + y + x - y = 15 + 1$

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$\sf \longmapsto 2x = 16$

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$\sf \longmapsto x = \dfrac { 16 } { 2 }$

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$\bf \dashrightarrow x = 8$

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$\underline{\bold{\texttt{Putting x = 8 in (1)}}}$

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$\sf 8 + y = 15$

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$\sf \longmapsto y = 15 - 8$

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$\bf \dashrightarrow y = 7$

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So,

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$\purple{\bold{Original \: Number \: will \: be :}}$

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$\red\longrightarrow$ $\sf 10(8) + (7)$

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• 87

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Hence the original number is 87

$\rule{200}5$

Answer 2

Answer:

ur num. is 87 ....................