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 18, find the original number.

Answer 1

the given sum of the digits is 12
so let the digits in ones place be x
∴ the digit in tens place is (12 – x)
∴the original number = 10(12 – x) + x = 120 – 9x
number formed by reversing the digits = 10x + (12 – x) 
                                                              =  9x + 12
given that number formed by reversing the digits is 54 greater than the original number.
⇒ 9x + 12 = (120 – 9x) + 54
                = 174 – 9x
⇒ 18x = 174 – 12
           = 162
∴ x = 9
∴ the original number = 120 – 9x = 120 – 9(9) = 39