Question

A two-digit number is such that the ten's digit exceeds twice the unit's digit by $2$ and the number obtained by inter-changing the digits is $5$ more than three times the sum of the digits. Find the two digit number.

Answer 1

Let the two digit number be $10x+y$ where $y$ is units digit and $x$ is ten's digit.

It is given that-

$x=2y+2$ ...$\left(1\right)$

and $10y+x=3(x+y)+5$ ....$\left(2\right)$

an solving equation $\left(2\right)$ and $\left(1\right)$

$10y+x=3x+3y+5$

$\Rightarrow 7y-2x=5$

$\therefore 7y-2(2y+2)=5$

$3y-4=5$

$3y=9$

$y=3$

and $x=2y+2=6+2=8$

the two digit number is $83$