A team of 8 persons takes part in a shooting competition. The best marksman in the team actually scored 85 points. If he had instead scored 92 points, the average score for the team would have been 84 points. What was the actual total number of points scored by the team?

Introduction / Context:
This problem uses the concept of averages in the context of a shooting competition. A team has a certain total score, and we are told how the team average would change if one member had scored a different number of points. From that hypothetical scenario, we work backward to compute the actual total score of the team. This type of problem is common in aptitude tests and reinforces the idea of adjusting totals when individual scores change.

Given Data / Assumptions:
- Number of persons in the team = 8.
- The best marksman actually scored 85 points.
- If he had scored 92 points instead, the average team score would have been 84 points.
- We must find the actual total points scored by the team with his real score of 85.

Concept / Approach:
The crucial idea is that changing a single member score changes the team total by the difference between the hypothetical and actual scores. The hypothetical situation gives us a clear value for the team total when the best marksman score is assumed to be 92. We then subtract the difference of 7 points (92 minus 85) to obtain the real team total. This adjustment method is much faster than trying to guess or set up a more complicated system.

Step-by-Step Solution:
Step 1: In the hypothetical scenario, the best marksman score is 92 and the team average is 84.Step 2: Total team score in this hypothetical case = average * number of persons = 84 * 8 = 672 points.Step 3: Compare the hypothetical score with the actual score of the best marksman.Step 4: Difference between assumed and actual score = 92 - 85 = 7 points.Step 5: This means the hypothetical team total exceeds the actual team total by 7 points.Step 6: Therefore actual team total = 672 - 7 = 665 points.Step 7: So the team scored 665 points with the best marksman actual performance.

Verification / Alternative check:
Let the sum of the scores of the other 7 members be S. In the hypothetical case, S + 92 = 672, so S = 580. In reality, the best marksman scored 85, so actual total = S + 85 = 580 + 85 = 665. This matches the earlier calculation, confirming that 665 is correct.

Why Other Options Are Wrong:
Totals like 672, 645 or 588 do not take into account the adjustment of 7 points between the actual and hypothetical scores. For instance, 672 is the total only in the imaginary situation where the marksman scores 92. The options 645 and 588 are too low and would lead to team averages that are inconsistent with the given information.

Common Pitfalls:
Many learners mistakenly think that 672 is the answer because it is directly obtained from 84 * 8. They forget that this total corresponds to the hypothetical score of 92, not the actual score of 85. Always adjust the total by the difference between the assumed and actual individual values when using such comparisons.

Final Answer:
The actual total number of points scored by the team is 665.