Question

Find two three-digit numbers whose sum is a multiple of $504$ and the quotient is a multiple of $6$.

Answer 1

Two three-digit number, Sum is a multiple of 504.

Sum should be 504, 1008 or 1512.

as 2016 cannot be sum of three-digit number.

Let one number $=x$.

So, other$=6x$ or $12x$

So, $x+6x=504$

$\Rightarrow 7x=504$

$\Rightarrow x\ne 72$

$\Rightarrow x+6x=1008$

$\Rightarrow 7x=1008$

$\Rightarrow x=144$

$\therefore$ other number$=6\times 144=864$

Hence, numbers are $144$ & $864$.