, 2022

The original ratio of red candies to blue candies is $3:5$, and so the number of red candies was
a positive integer multiple of 3, and the number of blue candies was the
same positive integer multiple of 5.

For example, there could have been $3\times1=3$ red candies and $5\times1=5$ blue candies, or $3\times2=6$ red candies and $5\times2=10$ blue candies, or $3\times3=9$ red candies and $5\times3=15$ blue candies, and so
on.

We continue these possibilities in the table below, and consider the
number of red and blue candies and the resulting ratio after three blue
candies are removed from the dish.

Possible numbers of red and blue candies
originally
3 red,
5 blue
6 red,
10 blue
9 red,
15 blue
12 red,
20 blue
15 red,
25 blue
18 red,
30 blue

Numbers of red and blue candies after 3
blue are removed
3 red,
2 blue
6 red,
7 blue
9 red,
12 blue
12 red,
17 blue
15 red,
22 blue
18 red,
27 blue

New ratio of the number of red candies
to blue
$3:2$
$6:7$
$9:12 =
3:4$
$12:17$
$15:22$
$18:27 =
2:3$

If the dish originally contained 18 red candies and 30 blue (note
that $18:30=3:5$), then when three
blue candies are removed, the ratio of the number of red candies to blue
candies becomes $18:27$ which is
equal to $2:3$, as required.

Therefore, there were $30-18=12$ more
blue candies than red candies in the dish before any candies were
removed.