The sum of the two-digit number is 9 The number formed by interchanging the order of the digits 27 more than the given number.Find the number.

Explanation

Let digit at unit's place be x and ten's place by y.
`therefore` Number = 10y + x
On reversing the digits, the new number = 10x + y
According to given condition,
x + y = 9 …(1)
and 10x + y = 27 + (10y + x)
implies 9x - 9y = 27
implies x - y = 3 ...(2)
Adding equations (1) and (2), we get
2x = 12
implies x = 6
Putting x = 6 in equation (1), we get
6 + y = 9 implies y = 3
Hence, the required number = 10y + x = 10 `xx` 3 + 6 = 36