Calculating Overall Pass Percentage from College Data

The question asks for the approximate overall pass percentage of the college based on the success rates in different academic programmes for boys and girls, given the total number of boys and girls in each programme.

We are provided with the percentage of successful students (Boys and Girls) for six different programmes: B.A., B.Sc., B.Com., B.B.A., B.C.A., and B.Tech.

The total number of students in each programme is fixed: 150 boys per programme and 120 girls per programme.

Steps to Calculate Overall Pass Percentage

1. Calculate the number of successful boys in each programme.
2. Calculate the number of successful girls in each programme.
3. Find the total number of successful boys across all programmes.
4. Find the total number of successful girls across all programmes.
5. Calculate the total number of successful students in the college (sum of total successful boys and girls).
6. Calculate the total number of students in the college (sum of total boys and girls across all programmes).
7. Calculate the overall pass percentage using the formula: $$ \text{Overall Pass Percentage} = \left( \frac{\text{Total Successful Students}}{\text{Total Students}} \right) \times 100\% $$

Detailed Calculation of Successful Students per Programme

Total boys per programme = 150

Total girls per programme = 120

• B.A.: Successful Boys = $150 \times \frac{80}{100} = 120$. Successful Girls = $120 \times \frac{60}{100} = 72$.
• B.Sc.: Successful Boys = $150 \times \frac{80}{100} = 120$. Successful Girls = $120 \times \frac{70}{100} = 84$.
• B.Com.: Successful Boys = $150 \times \frac{40}{100} = 60$. Successful Girls = $120 \times \frac{60}{100} = 72$.
• B.B.A.: Successful Boys = $150 \times \frac{90}{100} = 135$. Successful Girls = $120 \times \frac{60}{100} = 72$.
• B.C.A.: Successful Boys = $150 \times \frac{70}{100} = 105$. Successful Girls = $120 \times \frac{80}{100} = 96$.
• B.Tech.: Successful Boys = $150 \times \frac{70}{100} = 105$. Successful Girls = $120 \times \frac{60}{100} = 72$.

Total Successful Students in College

Total successful boys = $120 + 120 + 60 + 135 + 105 + 105 = 645$

Total successful girls = $72 + 84 + 72 + 72 + 96 + 72 = 468$

Total successful students = $645 + 468 = 1113$

Total Students in College

Total boys in college = $150 \text{ boys/programme} \times 6 \text{ programmes} = 900$

Total girls in college = $120 \text{ girls/programme} \times 6 \text{ programmes} = 720$

Total students in college = $900 + 720 = 1620$

Calculating the Overall Pass Percentage

Overall Pass Percentage = $ \left( \frac{1113}{1620} \right) \times 100\% $

Overall Pass Percentage $ \approx 0.687037 \times 100\% $

Overall Pass Percentage $ \approx 68.70\% $

Rounding to the nearest whole number, the approximate overall pass percentage is $69\%$.

Conclusion

Based on the calculations, the approximate overall pass percentage of the college is $69\%$. This matches option 2.

Revision Table: College Pass Data Summary

Additional Information: Understanding Weighted Averages

This problem involves calculating an overall percentage when different groups (boys and girls) have different total numbers and different pass percentages. This is similar to calculating a weighted average. The overall percentage is not simply the average of the individual pass percentages because the total number of students is different for boys and girls and within each program.

• A simple average would be summing the 12 percentages (6 for boys, 6 for girls) and dividing by 12, but this would be incorrect because it doesn't account for the actual number of students in each category.
• A correct approach is to calculate the total number of successful students and divide by the total number of students, as done in the solution. This gives a weighted average where the weights are the number of students in each category.

Understanding how to combine percentages from groups of different sizes is crucial in data interpretation questions.