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The sum of the digits of a two-digit number is $9$. When we intrchange the digits,it is found that the resulting new number is greater than the original number by $27$. What is two digit number?

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    $\begingroup$ Hi and welcome to the site! Since this is a site that encourages learning, you will get much more help if you show us what you have already done. Could you edit your question with your thoughts and ideas? $\endgroup$ – 5xum Aug 12 '14 at 9:43
  • $\begingroup$ Good answer by Shabbeh but you could do this by brute force method :) $\endgroup$ – MattAllegro Aug 12 '14 at 9:51
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$$\overline{ab}-\overline{ba}=27$$

$$(10a+b)-(10b+a)=27$$

$$a-b=3$$

and we know that :

$$a+b=9$$

so $a=6$ and $b=3$

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Let the two digits be $x$ and $9-x$. By condition, the reversed no. will be$10(9-x)+x$ and this is 27 more than the previous no. So, $$ $$ $10(9-x)+x=27+(9-x)+10x \implies 90-9x=36+9x \implies 18x=54 \implies x=3,$ so that the other no. is $9-x=9-3=6.$ Got it ???

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