Question

The ratio of a two digit number to the number obtained by reversing it's digits is 4:7 . The sum of digits is 9 ,find the number.

Answer 1

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

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

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• Ratio of original number to reversed two digit number is 4:7

• Sum of digits is 9

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

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

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

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

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

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$\sf \longmapsto \dfrac { 10x + y } { 10y + x } = \dfrac { 4 } { 7 }$

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$\sf \longmapsto 40y + 4x = 70x + 7y$

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$\sf \longmapsto 33y = 66x$

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$\underline{\bold{\texttt{Dividing the above equation by 33}}}$

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

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Also ,

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$\purple\longrightarrow$ $\sf x + y = 9$ -----(2)

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

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$\sf \longmapsto x + 2x = 9$

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$\sf \longmapsto 3x = 9$

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$\sf \longmapsto x = \dfrac { 9 } { 3 }$

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$\sf \longmapsto x = 3$

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$\underline{\bold{\texttt{Putting x = 3 in (1)}}}$

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$\sf \longmapsto y = 2(3)$

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$\sf \longmapsto y = 6$

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$\underline{\bold{\texttt{Hence original number will be :}}}$

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$\sf \dag \: \: 10x + y$

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$\sf \dag \: \: 36$

$\rule{200}5$

Answer 2

Step-by-step explanation:

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