Question

The sum of the digits number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number

Answer 1

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

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

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• Sum of digits is 12

• Reversed number is greater than the original number by 54.

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

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$\purple\longrightarrow$ $\sf x + y = 12$

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$\purple\longrightarrow$ $\sf x = 12 - y$------(1)

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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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$\sf \longmapsto 10x + y + 54 = 10y + x$

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$\sf \longmapsto 9x - 9y + 54 = 0$

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

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$\sf \longmapsto x - y + 6 = 0$ -------(2)

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$\underline{\bold{\texttt{Putting x = 12 - y in (2)}}}$

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$\sf \longmapsto 12 - y - y + 6 = 0$

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$\sf \longmapsto 18 - 2y = 0$

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$\sf \longmapsto 2y = 18$

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$\sf \longmapsto y = \dfrac { 18 } { 2 }$

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$\sf \longmapsto y = 9$

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$\underline{\bold{\texttt{Putting y = 9 in (1)}}}$

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$\sf \longmapsto x = 12 - 9$

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$\sf \longmapsto x = 3$

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$\underline{\bold{\texttt{Hence original number will be :</p><p>}}}$

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$\purple\longrightarrow$ $\sf 10(3) + 9$

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$\bf \dashrightarrow 39$

$\rule{200}5$

Answer 2

Step-by-step explanation:

pls make it brainlest answer