Question

the digit in the tens placeof a two digit is three times that in the units place. if the digits are reversed , the new no will be 36 less than the original number .Find the original no.

pls help

Answer 1

If a number's ten digit is $x$ and the units digit is $y$, then you can write the number as $10x+y$.

Obviously, inverting the digits would lead to the number $10y+x$.

Since this new number is 36 less than the original, we have

$10y+x = 10x+y-36 \iff 9x-9y=36\iff x-y=4$

Since we also know that the digit in the tens place is three times that in the units place, we can add an equation to form a system:

$\begin{cases}x-y=4\\x=3y\end{cases}\iff 3y-y=4\iff y=2$

And thus $x=2\cdot 3=6$