An unknown frequency x produces 8 beats per seconds with a frequency of 250 Hz and 12 beats with 270 Hz source, then x is

Since source of frequency x gives 8 beats per second with frequency 250 Hz, it's possible frequency are 258 or 242. As source of frequency x gives 12 beats per second with a frequency 270 Hz, it's possible frequencies 282 or 258 Hz. The only possible frequency of x which gives 8 beats with frequency 250 Hz also 12 beats per second with 258 Hz.