Initially, freq(B) could be 512±5, i.e., 517 Hz or 507 Hz. Filing a tuning fork increases its frequency. If freq(B) was 517 Hz, filing would increase it further, increasing the beat frequency. If freq(B) was 507 Hz, filing would increase it towards 512. Since the beat frequency remains 5, this cannot be right. Let's re-read. Ah, "B is filled", not "filed". This means mass is added, so frequency decreases. If freq(B) was 517 Hz, adding mass would decrease it towards 512, which would decrease the beats. If freq(B) was 507 Hz, adding mass would decrease it further, increasing the beats. The question is flawed. Assuming "filed", the original frequency must be 507 Hz.