Get both batteries checked (they check each cell with a sort of indicator which changes colour depending on the state of the cell) - sometimes even new ones have manufacturing defects. If the batteries are fine then check if there is any parasitic load across the battery terminals. This load basically means that even after you take the key out, there is some path for the current to flow. If you understand electrical basics this simply involves disconnecting the cable that goes into the +ve pole of the battery and connecting an ammeter between the cable and the +ve pole WITHOUT turning on the battery. Ideally the meter should read zero. If the meter reads anything in excess of 500mA you could have a parasitic load which will drain the battery if the engine (and hence the alternator) is not running. Assuming a typical rating of 50Ah for the battery, a load of 500mA without any charging will discharge the battery within 100 hours, that's approx. 4 days. Be very careful if you do this yourself, a car battery has enough juice to sustain in excess of 200A for a short duration - that's a serious hazard. Better would be to let the mechanic check the things.
S = k.I^2, where S is the amount of stupidity a species possesses, I is the intelligence the species has and k is the universal constant of stupidity.
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