Question

the sum of two digit number is 17 on reversing its digits the new number is 9 more than original number find the number , with solution

Answer 1

$\huge\underline{\underline{\bf\bigstar ANSWER \bigstar }}$

Let the digit in tens place be x and digit in ones place be y .

Original number = 10x + y

Reversed number = 10y + x

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According to the first condition ,

  $\sf\hookrightarrow x+y = 17 \ \ \ \ \ \ \ \ \ \ \ \ \ .........(1)$

According to the second condition ,

  $\sf \hookrightarrow 10x+y+9=10y+x\\\\\hookrightarrow 10x-x +y-10y = -9\\\\\hookrightarrow 9x-9y = -9\\\\\hookrightarrow x-y =-9 \ \ \ \ \ \ \ \ \ \ \ ..........(2)$

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Add Eq(1) and Eq(2) ,

   $\sf\longrightarrow 2x = 16$

   $\longrightarrow \bf x = 8$

Substitute the value of x in Eq (1) ,

  $\longrightarrow \sf 8+y = 17\\\\\longrightarrow \bf y = 9$

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Original number = 89

HOPE IT HELPS U .........  :)