Math, asked by jugesh8888, 10 months ago

the sum of a two digit number and the number formed by interchanging the digits is 187.the new number formed is 9 less than the original number.Find the original number.......
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Answers

Answered by Anonymous
20

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

 \:\:

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

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  • Sum of a two digit number and the number formed by interchanging the digits is 187

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  • New number formed is 9 less than the original number.

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

 \:\:

  • 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

 \:\:

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

 \:\:

The sum of a two digit number and the number formed by interchanging the digits is 187

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So,

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 \sf \longmapsto 10x + y + 10y + x = 187

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 \sf \longmapsto 11x + 11y = 187

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 \sf \longmapsto 11(x + y) = 187

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 \sf \longmapsto x + y = \dfrac { 187 } {11 }

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 \sf \longmapsto x + y = 17 ------(1)

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Also,

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New number formed is 9 less than the original number

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 \sf \longmapsto 10x + y -(10y + x ) = 9

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

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 \sf \longmapsto 9x - 9y = 9

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 \sf \longmapsto 9(x - y) = 9

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 \sf \longmapsto x - y = \dfrac { 9 } { 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 = 17 + 1

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 \sf \longmapsto 2x = 18

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 \sf \longmapsto x = \dfrac { 18 } { 2 }

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 \bf \dashrightarrow x = 9

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

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 \sf \longmapsto 9 + y = 17

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 \sf \longmapsto y = 17 - 9

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 \bf \dashrightarrow y = 8

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 \red{\bold{Original \: number \: is}}

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  • 10(9) + 8

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 \bf \dag \: \: 98

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\rule{200}5

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