CEMC Cayley, 2025

Let the number of red marbles be $7n$, the number of yellow marbles be $3n$, and the number of green marbles be
$5n$.

Note that the ratio of the number of red marbles to the number of yellow
marbles to the number of green marbles is $7n:3n:5n=7:3:5$, as is given.

The total number of marbles is 600, and so $7n+3n+5n=600$ or $15n=600$, and so $n=\dfrac{600}{15}=40$.

Thus, the number of red marbles is $7n=7(40)=280$, the number of yellow
marbles is $3n=3(40)=120$, and the
number of green marbles is $5n=5(40)=200$.

If $20$ marbles of each colour are
removed, the number of red marbles is $280-20=260$, the number of yellow marbles
is $120-20=100$, and the number of
green marbles is $200-20=180$. In
this case, the new ratio of the number of red marbles to the number of
yellow marbles to the number of green marbles is $260:100:180=26:10:18=13:5:9$.