Comment: this question is a bit confusing, since none of the answers seems to directly explain how a shift to the right in the dissociation curve results in more oxygen delivered to tissue. Therefore, we'll try to choose the least wrong option...
This answer came out a bit long, so here's a TL;DR for you. I chose
and here's why:
Although not stated explicitly, the pH in question is most probably the blood pH (this is a rather well-known graph from biochemistry undergrad studies). It shows that when blood pH drops or rises, the amount of %O2 saturation of hemoglobin deviates from the norm accordingly.
First of all, regarding your rule-of-thumb, it might be misleading in this context, since it may be true in both normal conditions and pathological conditions, depending on the site of measurement:
- Under normal conditions, general blood pH is around 7.4 (7.35-7.45), blood pH in the tissues is around 7.2 (due to increased pCO2 resulting from cellular metabolism), and blood pH in the lungs is around 7.6 (due to the release of CO2 in the lungs for expiration, which results in lower pCO2 in the lungs) - see this reference and its references.
- Under pathological conditions, general blood pH may rise above 7.45 (alkalosis) or fall under 7.35 (acidosis), regardless of the site of measurement [reference]. This means that a dissociation curve under abnormal blood pH value does not necessarily relate to normal conditions in a certain body site, but may also relate to a pathological condition in which blood pH is abnormal in general.
I believe the graph represents the latter situation, i.e. how hemoglobin behaves under the pathological states of acidosis (lower blood pH = right-shift) and alkalosis (higher blood pH = left-shift) compared to the normal state, since it depicts the change in %O2 saturation over the physiological range of pO2 and the curve is continuous (a depiction of blood pH only in the tissues or the lungs would not have resulted in a curve, since pO2 does not change significantly in each site, certainly not over the physiological range).
Now let us consider the possible answers:
- Option A - The distance between the curves at 100 mmHg is less than the distance at 40 mmHg. This seems to be true in it's own right. However, other than describing the situation, it does not explain explicitly anything. It essentially says that the difference between oxygen release in the tissues is more pronounced than the difference in oxygen binding in the lungs, when comparing normal blood pH and acidosis. We can infer that if the right-shifted curve is below the normal and left-shifted curve, it means that less Oxygen is bound in the tissues (and also everywhere else, since this trend is consistent), i.e. Hemoglobin is less saturated, i.e. more Oxygen is released in the tissues in a state of acidosis than in any other state.
- Option B - The distance between the curves at 100 mmHg is more than the distance at 40 mmHg. This is merely the opposite of A, and therefore is untrue by the same amount that A is true.
- Option C - On the right-shifted curve, Hb will pick up more O2 in the lungs. This is a bit trickier. This option suggests that when pH is lower-than-normal (acidosis), more Oxygen will bond to Hemoglobin in the lungs. However, by observing the graph, we can see that the right-shifted curve is always below the other curves (both the normal and the alkalosis curves). This is also true in high values of pO2, which are present in the lungs. This renders this statement incorrect in itself, and it also does not explain why more oxygen is released in the tissues.
- Option D - On the right-shifted curve, Hb will pick up less O2 in the lungs. Based on the analysis of option C, it should be rather evident that the opposite must be true. That is, if the right-shifted curve is always below the other curves, including in high pO2 values, then under this condition Hemoglobin is bound to pick up less oxygen in the lungs than in any of the other conditions. Therefore, this statement is correct, but it does not explain why more oxygen is released in the tissues.
According to the section titled The influence of pH on oxygen-hemoglobin binding in this excellent reference, "the presence of a low pH locks it [hemoglobin] in an unreceptive state, preventing it from binding oxygen molecules". This means that Hemoglobin's affinity to oxygen will be reduced, so that more oxygen will be released (in other words, less will be bound) in the tissues and less oxygen will be bound in the lungs. The two "less" in the previous sentence are in accordance with the curve of pH=7.2 being below the other two curves over the entire range of pO2. I highly recommend reading the above reference through and observing the figures.
To sum up, none of the possible options is satisfying enough, but option A seems to be the least wrong or unrelated to the situation described, so I would choose it.