Solving a Mathematical Puzzle: Finding the Total Number of Students Based on Average Marks

Mathematical puzzles and problems are not only fun but also a great way to sharpen your analytical skills. In this article, we will explore a case involving the incorrect entry of marks and how it affected the average of a class. By solving this problem, we can gain a deeper understanding of how changes in individual scores can influence class averages.

The Problem Statement

A student's mark was wrongly entered as 110 instead of 98. Due to this mistake, the average marks of the class got increased by 2/5. The task is to determine the total number of students in the class.

Step-by-Step Explanation

The problem can be broken down into simpler steps to find the solution.

Step 1: Understanding the Variation in Total Marks

The variation in total marks due to the mistake can be calculated as:

Variation of marks in total 110 - 98 12

Step 2: Analyzing the Variation in Average Marks

The average marks of the class got increased by 2/5. Therefore, the variation in average marks can be expressed as:

Variation of marks in average 2/5

Step 3: Calculating the Total Number of Students

The total number of students can be determined from the variation in marks and the variation in average marks:

Number of students Variation of marks in total / Variation of marks in average

In this case:

Number of students 12 / (2/5) 12 * (5/2) 30

The division by 2/5 is equivalent to multiplying by its reciprocal (5/2), resulting in 30.

Therefore, the total number of students in the class is 30.

Conclusion

By solving this problem, we have demonstrated how a simple arithmetic method can be used to determine the number of students based on a change in their average marks caused by an incorrect entry of a single student's mark. Such puzzles are not only beneficial for improving mathematical acumen but also for enhancing logical reasoning and problem-solving skills.

Keywords: mathematical puzzles, average marks, student number