Question

Average mark of 8 students in the class is 91 when one more student is included the average decreased by 1 find the mark scored by the new student ?

• A. 72
• B. 82
• C. 98
• D. 50

Answer 1

Answer:

B. 82

Understanding Average Problems in Competitive Exams

• The concept of average (also known as the mean) is fundamental in quantitative aptitude sections of competitive exams. It is calculated as the sum of all observations divided by the number of observations.
• Formula: Average = (Sum of Observations) / (Number of Observations)

Step-by-Step Calculation:

1. Calculate Initial Total Marks: Initially, there are 8 students with an average mark of 91. Using the formula, the total marks for these 8 students can be found:
   • Total Marks = Average × Number of Students
   • Total Marks = 91 × 8 = 728
2. Determine New Average and Number of Students: When one more student is included, the total number of students becomes 8 + 1 = 9. The average mark decreases by 1, so the new average is 91 - 1 = 90.
3. Calculate New Total Marks: With the new number of students and the new average, calculate the updated total marks for all 9 students:
   • New Total Marks = New Average × New Number of Students
   • New Total Marks = 90 × 9 = 810
4. Find the New Student's Mark: The difference between the new total marks and the initial total marks will give the mark scored by the newly included student.
   • Mark of New Student = New Total Marks - Initial Total Marks
   • Mark of New Student = 810 - 728 = 82

Key Facts and Tips for Average Questions:

• Shortcut Method (Deviation Method): This type of problem can often be solved quickly using a deviation approach. If the new student had scored 91 (the old average), the average would not change. Since the average decreased by 1 for 9 students, it means the new student's score was 9 less than 91. So, 91 - (9 students × 1 mark decrease) = 91 - 9 = 82.
• Impact of Inclusion/Exclusion: Understand how adding or removing an observation affects the average. If the added value is less than the current average, the average decreases; if it's more, the average increases.
• Practice Variations: Be prepared for variations where a person leaves, or an incorrect value is used and needs correction. The core principle of finding the 'sum' remains crucial.
• Common Mistakes: A common error is forgetting to update the 'number of observations' when a new person is added or removed.