Question

A two digit number is $4$ more than $6$ times the sum of its digits. If $18$ is subtracted from the number, the digits are reversed. Find the number.

Answer 1

Let $x=$ ones digit and $y=$tens digit

According to the question $,$

$\therefore x+10y=6(x+y)+4\Rightarrow 10y=6x+6y+4-x\Rightarrow 4y=5x+4$

And $,$ from if $18$ is substracted from the number $,$ the digits are reversed $,$

$\therefore x+10y-18=y+10x\Rightarrow 10y-18=y+9x\Rightarrow 9y-18=9x\Rightarrow y-2=x$

Substitute $x$ value into $:$

$4y=5x+44y=5(y-2)+44y=5y-6y=6$

Substitute $y$ into $:$

$\therefore y-2=x\Rightarrow 6-2=x\Rightarrow 4=x$

$\therefore$ The number is $64.$