A tuning fork A produces 4 beats/s with another tuning fork B of...

There are 4 beats between $A$ and $B$, therefore the possible frequencies of $A$ are 316 or 324 that is $(320 \pm 4) \mathrm{Hz}$. When the prong of $A$ is filed, its frequency becomes greater than the original frequency. If we assume that original frequency of $A$ is 324 then on filing its frequency will be greater than 324 . The beats between $A$ and $B$ will be more than 4 . But it is given that the beats are again 4 , therefore, 324 is not possible. Therefore, required frequency must be 316 Hz . (This is true, because on filing the frequency may increase so as to give 4 beats with $B$ of frequency 320 Hz).