The sum of the digits of a 2-digit number is 8. If the digits are reversed, the new number increases by 18. Find the number.

Given :

The sum of the digits of a 2-digit number is 8. If the digits are reversed, the new number increases by 18.

To find :

We have to find the number.

Solution :

Let the number be $10x+y$.

$x+y=8$.....(i)

It is given that when the digits are reversed, the new number increases by 18.

Therefore,

$10y+x= (10x+y)+18$

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

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

$9y-x(10-1)=18$

$9y-9x=18$

$9(y-x)=18$

$y-x=\frac{18}{9}$

$y-x=2$.....(ii)

Adding equations (i) and (ii), we get,

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

$2y=10$

$y=\frac{10}{2}$

$y=5$

$x+5=8$

$x=8-5$

$x=3$

The original number is $10(3)+5=30+5=35$.

Therefore, the number is 35.