Question

The sum of a two digit number and the number obtained by reversing the order of the digits is 99. Find the number, if the digits differ by 3.

Answer 1

Let the digits in the tens place be x and the digit in the units place be y.
∴ Number = 10x + y
Number on reversing the digits = 10y + x
The difference between the digits = x - y or y - x
Given : ( 10x + y ) + ( 10y + x ) = 99
⇒ 11x + 11y = 99
⇒ x + y = 9                 ...(1)

x - y = 3                      ...(2)
or y - x = 3                  ...(3)
On solving equations (1) and (2), We get
2x = 12 ⇒ x = 6
So, y = 3

On solving equation (1) and (3), We get
2y = 12 ⇒ y = 6
So, x = 3
Number = 10x + y = 10(6) + 3 = 63
or Number = 10x + y = 10(3) + 6 = 36
∴ Required number = 63 or 36.