The unknown frequency of the tuning fork can be
= 310 ± 4
or f = 314 or 306 Hz
Suppose f = 314 Hz
On filing, let it becomes = 318 Hz.
When it sounded together with a fork of frequency 310 Hz, beats frequency will be more than 4 per second. Therefore unknown frequency can not be 314 Hz.
Now suppose f = 306 Hz.
On filing, let it becomes = 314 Hz.
When it sounded again with a fork of frequency 310 Hz it gives 4 beats per second. So unknown frequency must be 306 Hz.