Let the digit in unit’s place be ‘x’ and the digit in ten’s place be ‘y’.
|
Digit in tens place |
Digit in units place |
Number |
Sum of the digits |
Original
number |
y |
x |
10y + x |
y + x |
Number obtained by
interchanging the digits |
x |
y |
10x + y |
x + 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
