# If 18 is added to a two-digit number, the digits are reversed. The sum of the digits is 8. What is the original number?

#### Answer:

$35$

#### Explanation:

Let $x$ & $y$ be respectively unit & tenth digits of two-digit number then the number will be

$10 y + x$

Condition 1: sum of digits is $8$ hence

$x + y = 8 \setminus \ldots \ldots \ldots \left(1\right)$

Condition 2: When $18$ is added to the number $10 y + x$ then digits are reversed i.e. number becomes $10 x + y$ hence

$18 + 10 y + x = 10 x + y$

$9 x - 9 y = 18$

$x - y = 2 \setminus \ldots \ldots \ldots . \left(2\right)$

Adding (1) & (2) as follows

$x + y + x - y = 8 + 2$

$2 x = 10$

$x = 5$

Setting $x = 5$ in (1), we get

$5 + y = 8$

$y = 3$

hence the number is

$10 y + x$

$= 10 \setminus \cdot 3 + 5$

$= 35$