Find the product of the balls

If the probability of getting two balls of the same colour is the same as having two balls of different colours, then both probabilities are 0.5 (complementary events).

If the number of red balls is n, then the number of blue balls is (25 - n).

The probability of having two balls of the same colour:

$p(R, R) + p(B, B) = \frac {n}{25} × \frac {n - 1}{24} + \frac {25 - n}{25} × \frac {24 - n}{24} = 0.5$

$2n^2 - 50n + 600 = 300$

$n^2 - 25n + 150 = 0$

$(n - 15)(n - 10) = 0$

This means, that we have either 15 red balls and 10 blue balls or vice versa.

In either case, our answer should be:

$15 × 10 = 10 × 15 = \boxed {150}$