Navigator,
You are correct in saying that the arguments were going in a strange direction, but this was simply in response to the suggestion by tolipanebas that the entire circuit resistance would be due to a 48 ohm internal resistance for each battery.
You are also correct in stating that both A and B are correct. This is precisely why I stated that the question was defective.
Your earlier suggestion that I had erroneously introduced a load is however more problematic.
The questions specifies two 12 volt, 40 Ampere hour batteries connected in parallel. The options offered are combinations of 24v, 12V, 40 hours and 80 hours. We have all agreed that when connected in parallel the circuit voltage will be 12V. But the two choices of 40 hours and 80 hours imply two possible circuit resistances.
The batteries are connected in parallel, so each provides half of the total current. So if the life is 40 hours then we have 40 Ampere hours divided by 40 hours = 1 Amp from each battery. This gives 2a for the entire circuit. If a circuit voltage of 12 V results in a current of 2A then the resistance must be 12 volts divided by 2 amp, which is 6 ohms. So if the correct answer is 40 hours then the total circuit resistance must be 6 ohms. By applying the same logic it can be shown that for a life of 80 hours, the total circuit resistance must be 12 ohms. So total resistances of 6 and 12 ohms are implicit in the options offered in the question.
The problem with the question is that the total resistance is not stated, nor is the matter of whether or not internal resistances should be ignored.
Those members who have suggested that 80 hour is the more correct of the two options, appear to be assuming that the original condition (when the 40 Ah capacity was measured) was 1 Amp. But there is no justification for this assumption.
The fact that the batteries are connected in parallel certainly implies that each will provide half of the circuit current. This in turn will have an effect on their life in the circuit. This effect is however not as obvious as it might at first appear. The critical question to consider is "what was the original condition?".
To illustrate this let's just assume that the total resistance is a 12 ohm resistor and the internal resistances of the batteries are sufficiently small to be ignored.
a. A single battery would provide a circuit voltage of 12V and a current of 1A. This would give a life of 40 Ah divided by 1A which is 40 hours.
b. Two batteries connected in series would provide a circuit voltage of 24V and a current of 2A. This would give a life of 40 Ah divided by 2A which is 20 hours.
c. Two batteries connected in parallel would give a circuit voltage of 12V and a current of 1A. But each battery would provide only 1/2A. So the life of each battery would be 40Ah divided by 1/2A which is 80 hours.
If we use the alternative assumption that the total resistance is 6 Ohms then the results will be as follows:
a. A single battery would provide a circuit voltage of 12V and a current of 2A. This would give a life of 40 Ah divided by 2A which is 20 hours.
b. Two batteries connected in series would provide a circuit voltage of 24V and a current of 4A. This would give a life of 40 Ah divided by 4A which is 10 hours.
c. Two batteries connected in parallel would give a circuit voltage of 12V and a current of 2A. But each battery would provide only 1A. So the life of each battery would be 40Ah divided by 1A which is 40 hours.
So both the 40 hour and 80 hour life are equally justifiable.
For those preferring to skip the analysis and simply assume that "putting two batteries in parallel reduces the current from each by half, so the life is doubled", the above figures might be surprising. Comparing a single battery with two in parallel does indeed double the life. But comparing two in series with two in parallel gives 4 times the life.