Aditya sent us a very well explained solution to this problem:

Tim has 50% blue, 35% red, 10% white and 5% union jacks.
Beth has 40% blue, 32% red, 20% white and 8% union jacks.

In fractions, this is:

T = 1/2 blue, 7/20 red, 1/10 white & 1/20 union jack.
= 10/20 blue, 7/20 red, 2/20 white and 1/20 union jack.
Therefore Tim has 20 flags. B = 2/5 blue, 8/25 red, 1/5 white & 2/25 union jack.
= 10/25 blue, 8/25 red, 5/25 white and 2/25 union jack.
Therefore Beth has 25 flags.

Now, we know that Beth has more flags than Tim. Beth has one more red flag, and both have the same number of blue flags. Between them, they have 3 union jacks.