2450 boys and 1750 girls are examined in a test; 42% of the boys and 36% of the girls pass the test. The percentage of the total who failed is?

Appeared in: RRB Nsg. Superintendent 21 July 2019 (shift 1st)

Explanation

The question asks for the overall failure percentage, which is a weighted average based on the number of students in each group (boys and girls).
First, calculate the number of students who failed in each group. The failure percentage for boys is 100% - 42% = 58%, and for girls is 100% - 36% = 64%.
Number of failed boys = 58% of 2450 = 0.58 × 2450 = 1421.
Number of failed girls = 64% of 1750 = 0.64 × 1750 = 1120.
The total number of failed students is 1421 + 1120 = 2541.
The total number of students is 2450 + 1750 = 4200.

Option A: This value likely results from a calculation error when determining the number of failed students or during the final division.
Option B: This value is incorrect and likely stems from a miscalculation, possibly in multiplying the percentages or summing the totals.
Option D: This value is very close to the simple average of the two failure percentages (58% and 64%), which is 61%. Taking a simple average is a common mistake that ignores the different number of boys and girls.

Visual 1: Infographic: A flowchart demonstrating the steps to calculate a weighted average. It would show branching paths for each subgroup (boys, girls), calculating the number of failures in each, combining them for a total, and then dividing by the total population.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating a weighted average percentage from different subgroups as background academic context rather than a clinical decision trigger.
This type of calculation is fundamental in data analysis and is frequently used in fields like epidemiology to determine overall prevalence or incidence rates from different population subgroups (e.g., calculating the overall infection rate in a hospital based on rates in different wards).
Understanding weighted averages is crucial for accurately interpreting statistics and research findings, preventing misinterpretations that can arise from simply averaging percentages from groups of different sizes.
What if? If the number of boys and girls were equal (e.g., 2000 each), the overall failure percentage would be the simple average of the individual failure percentages: (58% + 64%) / 2 = 61%.

How to Approach the Question

First, carefully read the question to identify all the given values: number of boys, number of girls, pass percentage for boys, and pass percentage for girls.
Note that the question asks for the percentage of students who failed. This requires converting the given pass percentages into fail percentages (100% - pass %).
Calculate the absolute number of failures for each group by multiplying the group's total number by its failure percentage.
Sum the number of failures from each group to get the total number of failed students.
Sum the number of students from each group to get the total number of students.
Finally, divide the total number of failures by the total number of students and multiply by 100 to find the overall failure percentage.

Concept Tested & Keywords

Concept Tested: Calculating a weighted average percentage from different subgroups.
Stem keywords: boys, girls, examined, test, pass, failed, percentage
Lead-in keywords: percentage of the total who failed

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Practise the full RRB Nsg. Superintendent 21 July 2019 (shift 1st)

Attempt every question from this paper in a timed mock, then review the full solution for each one.