Question

The sum of the digits of a two digit number is 8. when 18 is added to the number, the digits are reversed. find the number?

Answer 1

Hence..the number is 35.

Answer 2

Answer:

Let the digit at one's place be x

Sum of digits = 8

$\therefore$ Digits at ten's place will be 8-x

Original number =

$10(8 - x) + x$

$80 - 10x + x$

$80 - 9x$

Reversed Number =

$10(x) + (8 - x)$

$10x + 8 - x$

$9x + 8$

According to Question :

$80 - 9x + 18 = 9x + 8$

$- 9x - 9x = 8 - 18 - 80$

$- 18x = - 10 - 80$

$- 18x = - 90$

$x = \frac{ - 90}{ - 18}$

$x = 5$

Original Number = 80 - 9 × 5 = 80 - 45=35