The following table shows the number of students (Boys and Girls) and the percentage of girls who passed in a 10+2 examination from six different schools (A-F) in the year 2023 and 2024. Based on the data in the table, answer the questions that follow.
School-wise Details of Students Passing in a 10+2 examination
School Year Year 2023 Year 2024 Number of Passed Students Percentage of Passed Girls Number of Passed Students Percentage of Passed Girls A 500 46% 550 44% B 600 42% 640 40% C 650 56% 560 45% D 720 60% 800 48% E 600 54% 840 55% F 650 50% 750 36%
Analyzing 10+2 Exam Data: Girls Passing Percentage
This problem requires us to compare the performance of students across different schools based on the provided data table. We need to find the average number of girls who passed the 10+2 examination in the year 2024 across all six schools (A-F). Then, we must express this average as a percentage of the total number of students who passed from School A in the year 2023.
Step 1: Calculate the Number of Girls Passed in 2024 for Each School
First, let's calculate the number of girls who passed from each school in 2024 using the total passed students and the percentage of girls passed.
- School A (2024): Total Passed = 550, Percentage of Girls Passed = 44%
Number of Girls = $550 \times \frac{44}{100} = 550 \times 0.44 = 242$ - School B (2024): Total Passed = 640, Percentage of Girls Passed = 40%
Number of Girls = $640 \times \frac{40}{100} = 640 \times 0.40 = 256$ - School C (2024): Total Passed = 560, Percentage of Girls Passed = 45%
Number of Girls = $560 \times \frac{45}{100} = 560 \times 0.45 = 252$ - School D (2024): Total Passed = 800, Percentage of Girls Passed = 48%
Number of Girls = $800 \times \frac{48}{100} = 800 \times 0.48 = 384$ - School E (2024): Total Passed = 840, Percentage of Girls Passed = 55%
Number of Girls = $840 \times \frac{55}{100} = 840 \times 0.55 = 462$ - School F (2024): Total Passed = 750, Percentage of Girls Passed = 36%
Number of Girls = $750 \times \frac{36}{100} = 750 \times 0.36 = 270$
Step 2: Calculate the Total Number of Girls Passed in 2024
Sum the number of girls passed from all six schools in 2024:
Total Girls Passed (2024) = $242 + 256 + 252 + 384 + 462 + 270 = 1866$
Step 3: Calculate the Average Number of Girls Passed in 2024
Find the average by dividing the total number of girls passed by the number of schools (which is 6):
Average Girls Passed (2024) = $\frac{\text{Total Girls Passed (2024)}}{\text{Number of Schools}}$
Average Girls Passed (2024) = $\frac{1866}{6} = 311$
Step 4: Identify the Number of Students Passed from School A in 2023
From the table, the number of students who passed from School A in the year 2023 is 500.
Step 5: Calculate the Required Percentage
Now, we need to find what percentage the average number of girls passed in 2024 (311) is of the number of students passed from School A in 2023 (500):
Percentage = $\left( \frac{\text{Average Girls Passed (2024)}}{\text{School A Passed Students (2023)}} \right) \times 100$
Percentage = $\left( \frac{311}{500} \right) \times 100$
Percentage = $\frac{311}{5}$
Percentage = $62.2\%$
Therefore, the average number of girls who passed in the year 2024 from all the six schools is 62.2% of the number of students who passed from School A in the year 2023.
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