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 \(258 Hz.\)