Question

sum of the digits of a 2 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

Answer 1

Given sum of the digits is 12 Let the digits in ones place be x Hence 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