Question

A number consists of two digits in which the tens digit exceeds the units digit by $6$. The number itself is equal to ten times the sum of digits. Find the number.

Answer 1

Let the number is $10y+x$ where x is the unit digit and y is the ten's digit. Then by the given question,

$y=x+6$

$10y+x=10(x+y)$

$10y+x=10x+10y$

$x-10x=0\Rightarrow x=0$

$y=0+6\Rightarrow y=6$

the given number is

$10\times 6+0=60$