Question

A two-digit number is $3$ more than $4$ times the sum of the digits. If $18$ is added to the number, the digits are reversed. Find the number.

Answer 1

Let the tens and unit digit of number are $x,y$

First condition :

$\Rightarrow 10x+y=3+4(x+y)$

$\Rightarrow 6x-3y=3$

$\Rightarrow 2x-y=1$

Second condition :

$\Rightarrow 10x+y+18=10y+x$

$\Rightarrow x-y=-2$

Subtract resultant equations ;

$\Rightarrow x=3$

$\Rightarrow y=5$

$\therefore$two digit number =$35$