he 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

   20

3. C

   40

4. D

   45

Appeared in: NORCET 6 mains-2024

Explanation

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• The core principle is that the sum of all parts must equal the whole.
• First, calculate the total marks for all 20 students by multiplying their average mark by the number of students: 45 × 20 = 900.
• Next, calculate the total marks for the known subgroups: the first 10 students (10 × 50 = 500) and the last 9 students (9 × 40 = 360).
• The sum of marks for these 19 students is 500 + 360 = 860.
• The marks of the single remaining student (the 11th) is the difference between the total sum and the sum of the subgroups: 900 - 860 = 40.

Why Other Options Were Wrong

• Option A: This is an incorrect result obtained from a calculation error.
• Option B: This is an incorrect result obtained from a calculation error.
• Option D: This value represents the average marks of the entire group of 20 students, not the specific marks obtained by the 11th student.

Related Visual

• Visual 1: Flowchart: A visual flowchart can illustrate the calculation process: (1) Calculate Total Sum (20 × 45 = 900). (2) Calculate Subgroup Sums (10 × 50 = 500 and 9 × 40 = 360). (3) Subtract Subgroup Sums from Total Sum (900 - (500+360)). (4) Final Answer (40).

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating a missing value using the concept of arithmetic mean (average) as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of problem tests numerical reasoning and logical deduction, which are essential skills for nurses.
• Nurses frequently perform calculations for medication dosages, IV drip rates, and fluid balance, all of which require accuracy and an understanding of basic mathematical principles.
• What if the question stated the 'last 10' students instead of the 'last 9'? In that case, the groups would overlap (the 10th student would be in both), and the problem could not be solved as stated, highlighting the need to carefully analyze the composition of subgroups.

How to Approach the Question

• First, identify all the numerical data provided: the total number of students and their overall average, and the size and average of the two subgroups.
• Recognize that the core relationship is: Sum of Values = Average × Number of Values.
• Calculate the total sum for the entire group (20 students). This is your 'whole'.
• Calculate the sum for each of the subgroups (the first 10 and the last 9 students). These are your 'parts'.
• Understand that the 'first 10' and 'last 9' students account for 19 out of the 20 students, leaving the 11th student as the missing piece.
• Subtract the sum of the parts from the whole to find the value of the missing piece: Total Sum - (Sum of Part 1 + Sum of Part 2).

Concept Tested & Keywords

• Concept Tested: Calculating a missing value using the concept of arithmetic mean (average).
• Stem keywords: average marks, 20 students, first ten, last nine, 11th student
• Lead-in keywords: What are

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QHcXCuNgax9ZS9NuWHQObY

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