Question

The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, then the digits interchange their places. Find the number

Answer 1

Let the digit in the units place be x. Then the digit in the tens place is `(9 -x)`
The number is `10 (9-x) + x = 90 - 9x`
The number formed by interchanging the digits is `10 x + 9 - x = 9x + 9`
Given that `90 - 9x - 27 = 9x + 9`
`rArr x = 3`
`:.` Units digit is 3, tens digit is `9 -3 = 6`, and the number is 63