The sum of number of a two-digit number is 8. If 36 is added to the number climate the number reversed. Discover the number.
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Given :
The sum of the digits of a two-digit number is 8, if 36 is included to the number the digits obtain reversed.
To discover :
We have actually to find the number.
Solution :
Let the number it is in $10x+y$.
$x+y=8$
It is additionally given the if 36 is added to the number the digits gets reversed.
Therefore,
$10x+y+36 = 10y+x$
$10y+x-10x-y = 36$
$10y-y+x-10x= 36$
$9y-x(10-1)=36$
$9y-9x=36$
$9(y-x)=36$
$y-x=frac369$
$y-x=4$
$y-x=4$ and $x+y=8$
Adding them,
$y-x+x+y=4+8$
$2y=12$
$y=frac122$
$y=6$
$x+6=8$
$x=8-6$
$x=2$
The initial number is $10(2)+6=20+6=26$.
Therefore, the number is 26.
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