Question

find two-three digit numbers whose sum is multiple of 504 and quotient is multiple of 6..

Answer 1

please interpret the que also

Answer 2

Say the two numbers are \(A\) and \(B\) such that \(A > B\) :

\(\large A + B = 504t\)
\(\large \dfrac{A}{B} = 6 \implies A = 6B \)


combining above both you get :
\(\large 6B + B = 504t \implies B = 72t\)

Answer 3

plugin \(t = 1\), you get \(B = 72*1 = 72\)
But you want a 3 digit number, so discard this

Answer 4

pluging \(t = 2\), whatd do you get ?

Answer 5

144

Answer 6

yes, since it is a 3 digit number you're okay with B
how about A ?

Answer 7

use \(\large \dfrac{A}{B}=6\) to find \(A\)

Answer 8

432..?

Answer 9

yes,
t > 2 will not work, why ?

Answer 10

hey you get B = 144*6 = 864, right ?

Answer 11

cuz its 3 digit no