Ratio of Fish

For positive integers $m,n$ we have that there are $3m$ red fish and $4m$ blue fish in the small tank, as well as $3n$ red fish and $4n$ blue fish in the large tank.

There are then $3m + 4m = 7m$ fish in the small tank and $3n + 4n = 7n$ fish in the large tank. We are then given that $\dfrac{7n}{7m} = \dfrac{46}{5} \Longrightarrow \dfrac{n}{m} = \dfrac{46}{5}$ .

As there are $4m$ blue fish in the small tank and $3n$ red fish in the large tank, the desired ratio is

$\dfrac{4m}{3n} = \dfrac{4}{3 \times \dfrac{n}{m}} = \dfrac{4}{3 \times \dfrac{46}{5}} = \dfrac{4 \times 5}{3 \times 46} = \dfrac{10}{69}$ , i.e., the answer is $\boxed{10 : 69}$ .