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.
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