Question

The sum of the digits of a two-digit number is 12. If the new number formed by reversing
the digits is greater than the original number by 54, find the original number.
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Answer 1

Let the digit at ones place be x

digit at tens place = 12 – x

Hence the number = ( 12–x ) 10 + x

= 120 – 10x + x

= 120 – 9x

Reverse digit number = ( x × 10 ) + ( 12– x )

= 10x + 12 – x

= 9x + 12

According to question

9x + 12 = 120 – 9x + 54

9x + 9x = 174 – 12

18x = 162

x = 162 / 18

x = 9

Hence, original number = 120 – 9x

= 120 – 81

= 39