The average marks of 50 students in a class are 72. The average marks of boys and girls in that subject are 70 and 75 respectively. The number of boys in the class is:

1. A

   55

2. B

   15

3. C

   50

4. D

   30

Appeared in: SGPGI Nursing Officer-2024

Explanation

• The problem requires finding the number of individuals in a subgroup (boys) given the average of the whole group, the average of the subgroup, and the average of the other subgroup (girls).
• This is a weighted average problem that can be solved by setting up an algebraic equation or by using the Rule of Alligation.
• The Rule of Alligation provides a quick way to find the ratio of the quantities of the two subgroups. The difference between the girls' average and the mean average (75-72=3) and the difference between the mean average and the boys' average (72-70=2) gives the ratio of boys to girls.
• The resulting ratio of boys to girls is 3:2.
• With a total of 50 students and a ratio sum of 5 (3+2), the number of boys is calculated as (3/5) of 50, which is 30.

Why Other Options Were Wrong

• Option A: This option is logically impossible as the number of boys (55) cannot be greater than the total number of students in the class (50).
• Option B: If there were 15 boys, there would be 35 girls. The overall class average would be [(15 × 70) + (35 × 75)] / 50 = (1050 + 2625) / 50 = 73.5. This does not match the given class average of 72.
• Option C: If all 50 students were boys, the class average would be the same as the boys' average, which is 70. This contradicts the given class average of 72.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Weighted Averages and Rule of Alligation as background academic context rather than a clinical decision trigger.
• This question tests general aptitude and numerical reasoning, skills that are part of many competitive nursing entrance exams.
• While not a clinical scenario, proficiency in mathematics is crucial for nurses in daily practice for tasks like calculating drug dosages, titrating IV drips, and interpreting patient data.
• What if the total number of students was 100? Using the same 3:2 ratio of boys to girls, the number of boys would be (3/5) × 100 = 60.

How to Approach the Question

• First, identify the given values: the total number of students (50), the overall average (72), and the individual averages for the two subgroups (boys: 70, girls: 75).
• Recognize this as a weighted average problem. The Rule of Alligation is the most efficient method.
• Set up the alligation framework: Place the lower average (70) on the left and the higher average (75) on the right. Place the mean average (72) in the center.
• Subtract diagonally across the mean: (75 - 72) = 3 and (72 - 70) = 2.
• The results give the ratio of the quantities of the two groups. The ratio of Boys : Girls is 3 : 2.
• Calculate the number of boys using the ratio and the total number of students: Number of boys = [3 / (3 + 2)] × 50 = (3/5) × 50 = 30.

Concept Tested & Keywords

• Concept Tested: Weighted Averages and Rule of Alligation
• Stem keywords: average marks, 50 students, class average 72, boys average 70, girls average 75
• Lead-in keywords: number of boys

Question ID

QH8m5SSvUkBCRYpYejEYK_

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