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

Introduction / Context:
This question deals with averages and shows how changing one person's score affects the overall average of a group. It is a standard type of aptitude problem where you must think in terms of total points rather than only averages. Here, the score of the best marksman is hypothetically increased, and we are told how the team average would change, from which we can work backwards.

Given Data / Assumptions:

• There are 8 persons in the shooting team.
• The best marksman actually scored 85 points.
• If he had scored 92 points, the average score of the team would have been 84 points.
• We must find the actual total points scored by the team.

Concept / Approach:
The key idea is that average = total points / number of shooters. We do not know the actual average, but we know a hypothetical scenario: if one shooter scored 7 points more (92 instead of 85), then the team average would be 84. From that hypothetical average, we can find the hypothetical total, subtract the extra 7 points, and obtain the real total.

Step-by-Step Solution:
Number of shooters = 8.If the best marksman scored 92 points, the average of the team would be 84.Hypothetical total points = 84 * 8 = 672.Currently, he actually scores 85 points, which is 7 points less than 92.So the actual total is 672 - 7 = 665 points.Therefore, the total number of points that the team actually scored is 665.

Verification / Alternative check:
In the hypothetical case, extra points given to the best marksman are 7. That extra 7 points spread over 8 members increases the average by 7 / 8 = 0.875. If the final average is 84 in the hypothetical case, then the actual average must be 84 - 0.875 = 83.125. Multiplying 83.125 by 8 again gives 665 total points. This confirms that the earlier calculation is consistent.

Why Other Options Are Wrong:
Any total less than 665, such as 657 or 658, would correspond to a lower actual average and not give an exact increase of 7 points when moving to the hypothetical scenario. Similarly, a total like 678 or 672 does not match the description, since the hypothetical total was already calculated as 672. Only 665 correctly accounts for the 7 point difference between the real and hypothetical scores.

Common Pitfalls:
Some students wrongly assume that the current average is 84 or try to adjust the average directly without considering total points. Another typical mistake is to divide the 7 points by something other than 8 or to add rather than subtract it from the hypothetical total. Always remember to use total points = average * number of members and then account for the change step by step.

Final Answer:
The team actually scored a total of 665 points.