The sum of a two digit number and the number obtained by interchanging the digits is 99

Answer

Let the digit in unit’s place be ‘x’ and the digit in ten’s place be ‘y’. According to the given condition, the sum of a two digit number and the number obtained by interchanging its digits is 99.  ∴ 10y + x + 10x + y = 99  ∴ 11x + 11y = 99  Dividing both sides by 11,  x + y = 9  If y = 1, then x = 8  If y = 2, then x = 7 If y = 3, then x = 6 and so on. ∴ The number can be 18, 27, 36, … etc.

Let the two digit number be 10x + y. Number obtained on interchanging the digits = 10y + x. The sum of a two digit number and the number obtained by interchanging its digits  is 99.10x + y + 10y + x = 99⇒11x + 11y = 99⇒ x + y = 9With the given information, only one equation can be formed. So, the number can be

18, 81, 54, 45, 27, 72, 36, 63.