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

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Solution

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 $= 6 x$ or $12 x$
So, $x + 6 x = 504$
$\Rightarrow 7 x = 504$
$\Rightarrow x \neq 72$
$\Rightarrow x + 6 x = 1008$
$\Rightarrow 7 x = 1008$
$\Rightarrow x = 144$
$∴$ other number $= 6 \times 144 = 864$
Hence, numbers are $144$ & $864$ .

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

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 12xSo, x+6x=504⇒7x=504⇒x≠72⇒x+6x=1008⇒7x=1008⇒x=144∴ other number=6×144=864Hence, numbers are 144 & 864.

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