The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.
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 = 9
With the given information, only one equation can be formed. So, the number can be 18, 81, 54, 45, 27, 72, 36, 63.