Question

The units' digit of a two digit number is thrice its tens digit. If 36 is added to the number, the digits interchange their place. Find the number.

Answer 1

Let, the unit digit is $x$ and tens digit is $y$.
Then, $x=3y$.
The number would be $10y+x$.
The number obtained by reversing the digits is $10x+y$

If 36 is added to the number, digits interchange their places
Therefore,
$\Rightarrow 10y+x+36=10x+y$
$\Rightarrow 36=10x-x+y-10y$
$\Rightarrow 36=9x-9y$
$\Rightarrow 9(x-y)=36$
$\Rightarrow x-y=4$ _____(1)

Substituting the value of $x=3y$ in equation (1), we get
$\Rightarrow 3y-y=4$
$\Rightarrow 2y=4$
$\Rightarrow y=2$

Substituting the value of $y$ in equation (1), we get
$\Rightarrow x-2=4$
$\Rightarrow x=6$

Hence, the number is 26.