Question

The tens digit of a two digit number is two times the ones digit. If you interchange the digits and add the resulting number to original number you get 66. Find the original number.

Answer 1

$\text{Let the ones digit of the number be x.}$

$\text{Then, the tens digit will be 2x}.$

So, the number will be $(2x\times 10)+(x\times 1)=20x+x=21x$

$\text{On interchanging the digits, the}\text{number will be}(x\times 10)+(2x\times 1)=10x+2x=12x$

$\text{It is given that}21x+12x=66$

$\Rightarrow 33x=66$
$\Rightarrow x=\frac{66}{33}$
$\Rightarrow x=2$

Hence, ones digit of the number is 2 and tens digit is 4.
The original number is 42.