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%
Understanding the 10+2 Examination Data for Schools A-F
The question asks us to find the average number of boys who passed the 10+2 examination in the year 2024 across six different schools (A through F). We are given the total number of passed students and the percentage of girls who passed for each school in 2024.
Calculating Number of Boys Passed in 2024 for Each School
To find the number of boys who passed, we first need to calculate the number of girls who passed using the given percentage and then subtract this from the total number of passed students for each school.
The formula used is:
- Number of Girls Passed = (Percentage of Passed Girls / 100) × Total Number of Passed Students
- Number of Boys Passed = Total Number of Passed Students - Number of Girls Passed
School A (2024)
- Total Passed Students = 550
- Percentage of Passed Girls = 44%
- Number of Girls Passed = $\frac{44}{100} \times 550 = 0.44 \times 550 = 242$
- Number of Boys Passed = $550 - 242 = 308$
School B (2024)
- Total Passed Students = 640
- Percentage of Passed Girls = 40%
- Number of Girls Passed = $\frac{40}{100} \times 640 = 0.40 \times 640 = 256$
- Number of Boys Passed = $640 - 256 = 384$
School C (2024)
- Total Passed Students = 560
- Percentage of Passed Girls = 45%
- Number of Girls Passed = $\frac{45}{100} \times 560 = 0.45 \times 560 = 252$
- Number of Boys Passed = $560 - 252 = 308$
School D (2024)
- Total Passed Students = 800
- Percentage of Passed Girls = 48%
- Number of Girls Passed = $\frac{48}{100} \times 800 = 0.48 \times 800 = 384$
- Number of Boys Passed = $800 - 384 = 416$
School E (2024)
- Total Passed Students = 840
- Percentage of Passed Girls = 55%
- Number of Girls Passed = $\frac{55}{100} \times 840 = 0.55 \times 840 = 462$
- Number of Boys Passed = $840 - 462 = 378$
School F (2024)
- Total Passed Students = 750
- Percentage of Passed Girls = 36%
- Number of Girls Passed = $\frac{36}{100} \times 750 = 0.36 \times 750 = 270$
- Number of Boys Passed = $750 - 270 = 480$
Calculating the Average Number of Boys Passed in 2024
Now, we sum the number of boys who passed from all six schools in 2024 and divide by the number of schools (which is 6) to find the average.
Total Number of Boys Passed (2024)
Total Boys Passed = Boys (A) + Boys (B) + Boys (C) + Boys (D) + Boys (E) + Boys (F)
Total Boys Passed = $308 + 384 + 308 + 416 + 378 + 480 = 2274$
Average Number of Boys Passed (2024)
Average Boys Passed = $\frac{\text{Total Boys Passed}}{\text{Number of Schools}}$
Average Boys Passed = $\frac{2274}{6} = 379$
Therefore, the average number of boys who passed the 10+2 examination in the year 2024 from all six schools is 379.
Important Questions from Average
- Find the mean marks of the following distribution.
Marks obtained No. of students 25 5 30 6 35 3 40 1 - The average of first 169 even numbers is
- The average weight (in kg) of a family of five members whose weights are 40 kg, 49 kg, 56 kg, 74 kg and 35 kg is:
- The average of first 152 odd natural numbers, is:
The average runs scored by a batsman in 23 matches is 40. In the next 10 matches, the batsman scored an average of 16 runs. Find his average runs scored (rounded off to two decimals) in all the 33 matches.
