The average marks obtained by 20 students is 45. The average of first ten is 50 and of last nine is 40. What are the marks obtained by 11^th student?

1. A

   30

2. B

   25

3. C

   40

4. D

   45

Appeared in: NHM MP Staff Nurse - 2015

Explanation

• The total marks for all 20 students is calculated by multiplying the number of students by their average marks (20 × 45 = 900).
• The total marks for the first 10 students (10 × 50 = 500) and the last 9 students (9 × 40 = 360) are calculated similarly.
• The marks of the 11th student are found by subtracting the sum of the marks of the first 10 and last 9 students from the total marks of all 20 students.
• Calculation: 900 - (500 + 360) = 900 - 860 = 40.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. It may arise from an arithmetic error during subtraction, for example, incorrectly calculating 900 - 860.
• Option B: This is an incorrect calculation. This value does not logically result from the steps required to solve the problem.
• Option D: This value is the average marks of all 20 students, not the specific marks of the 11th student.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Average (Mean) Calculation as background academic context rather than a clinical decision trigger.
• This question assesses fundamental quantitative reasoning and problem-solving skills, which are essential for various competitive examinations.
• The concept of averages is widely used in data analysis across many disciplines, including analyzing patient data or research outcomes in healthcare.
• What if the average of the last nine students was 45? The total for the last nine would be 9 × 45 = 405. The 11th student's marks would then be 900 - (500 + 405) = -5, indicating an error in the problem statement as marks cannot be negative.

How to Approach the Question

• First, identify the different groups and their properties (number of students and average marks) given in the problem.
• The core formula to use is: Total = Average × Number of items.
• Calculate the total marks for the entire group (all 20 students).
• Calculate the total marks for the known subgroups (first 10 and last 9 students).
• The marks of the missing student (the 11th) is the difference between the total marks of the whole group and the sum of the marks of the subgroups.

Concept Tested & Keywords

• Concept Tested: Average (Mean) Calculation
• Stem keywords: average marks, 20 students, first ten, last nine
• Lead-in keywords: What are the marks

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QEr3cueve06biYmwOlfxRM

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