"Can anyone suggest a possible cure for this problem?"
Apart from keep on rejecting as "Unfit for purpose" and trying replacement(s) or getting a full refund, there's nothing you can do as the consumer.
Sadly, the symptom isn't unusual. As the price of these sorts of consumer-electronics keeps on falling through the floor, the quality drops in sympathy.
From your report, and if it's a constant-pitch, fairly low-frequency hum (to be specific, 100 Hertz, i.e. twice the mains frequency), it's most probably inadequate smoothing in the circuit which converts from mains AC to a few volts DC. These are standard, off-the-shelf chips used by many manufacturers (grey or otherwise!), so can affect all makes and models. (BTW, nothing to do with aerial sensitivity).
The manufacturers/retailers rely on most people running the volume so high that the hum is masked... Take it back (again) I'm afraid. :-(