Question

The sum of the digit of a 2 digit number is 9. On reversing the digit, the new number formed is less than the original number by 9

Answer 1

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

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

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• Sum of digits is 9

• Reversed number is 9 less than the original number.

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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 ten's digit be 'x'

Let the one's 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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$\bf\dashrightarrow x + y = 9$ ------(1)

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Also,

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

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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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$\bf \dashrightarrow x - y = 1$ -------(2)

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

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$\sf \longmapsto 2x = 10$

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$\sf \longmapsto x = \dfrac { 10 } { 2 }$

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$\sf \dashrightarrow x = 5$

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$\underline{\bold{\texttt{Putting x = 5 in (1)}}}$

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$\sf \longmapsto 5 + y = 9$

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$\bf \dashrightarrow y = 4$

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$\underline{\bold{\texttt{Original number will be:}}}$

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$\purple\longrightarrow$ $\bf 10(5) + 4$

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$\sf \longmapsto 54$

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$\rule{200}5$

Answer 2

Step-by-step explanation:

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