Given,

A bag contains six balls of different colours, two balls are drawn in succession with replacement,

The probability that both the balls are of the same colour will be $p=\frac{6}{36}$

Now Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is $q$,

So, probability will be $q=\frac{{}^{6}C_1\times {}^{5}C_1\times {}^{4}C_1}{6^4}=\frac{120}{1296}=\frac{5}{54}$

Now the ratio of $p \& q$ will be $\frac{p}{q}=\frac{9}{5}$

Now, on comparing with $\frac{p}{q}=\frac{m}{n}\Rightarrow m+n=14$