Commenting frequency spectrum of a sampled data the question below asked in my latest signal processing exam. I have no idea about it and i could not find any solution in literature. Could you please help me finding out the answer. Actually i believe that i am quite good at signal processing until this question.

A voltage signal is sampled digitally in the laboratory at three different sampling frequencies, and FFTs are performed on the sampled data. In all cases, 512 data points are taken. Here is a record of the observations: 
‒ Data sampled at 115 Hz: A peak appears in the frequency spectrum at 2 Hz, with amplitude close to 3.0 V. Another peak appears in the frequency spectrum at 45 Hz, with amplitude close to 1.0 V. 
‒ Data sampled at 280 Hz: A peak appears in the frequency spectrum at 48 Hz, with amplitude close to 3.0 V. Another peak appears in the frequency spectrum at 95 Hz, with amplitude close to 1.0 V. 
-Data sampled at 500 Hz: A peak appears in the frequency spectrum at 185 Hz, with 
amplitude close to 1.0 V. Another peak appears in the frequency spectrum at 232 Hz, 
with amplitude close to 3.0 V. 

Question: What are most likely the true frequencies (and their corresponding amplitudes) in the voltage signal.
Consider the 3V component first (note that aliassing only affects frequency, not amplitude, so the 3V component will have the same magnitude at whatever frequencies it is aliassed to):

For Fs = 115 Hz the 3V component shows up at 2 Hz, so it's real frequency could be any value which satisfies f = 115*k +/- 2, i.e.

  2 Hz
113 Hz
117 Hz
228 Hz
232 Hz
...


Do the same thing for Fs = 280 Hz, where we have f = 280*k +/- 48:

 48 Hz
232 Hz
328 Hz
512 Hz
608 Hz
...


And then again for Fs = 500 Hz:

232 Hz
268 Hz
732 Hz
...


We can see that the only frequency which corresponds in all 3 cases is 232 Hz, so it looks like we have a 3V component at f = 232 Hz.

You can now apply the same approach to identify the frequency of the 1V component.