https://file.aiquickdraw.com/mathbot/file/17301081680231oa6g5h1.jpg

Let's go through each question step by step to solve them.

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### Information provided in the problem:
1. **Courses**: BA, BCom, BSc, each with a course duration of 3 years.
2. **Ratio of total students in BA, BCom, and BSc** = \(6 : 7 : 9\).
3. **Total first-year students** = 1250.
4. **Total second-year students** = 12% less than first-year students.
5. **Difference between total students in first and second year** = Difference between total students in second and third year.
6. 40% of first-year students are in BSc.
7. The ratio of BA to BCom students in first year = \(7 : 8\).
8. BCom third-year students are 25% less than BCom first-year students.
   
Using these details, let’s solve each question individually.

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### Question 117
What percentage of total students are in the second year?

1. Let the number of students in the first year be \(1250\).
2. Since second-year students are 12% less than first-year students:
   \[
   \text{Second year students} = 1250 \times (1 - 0.12) = 1250 \times 0.88 = 1100
   \]
3. To find the percentage of total students in the second year:
   \[
   \frac{1100}{1250} \times 100 = 88\%
   \]

**Answer: None of the options exactly match 88% for Q117.**

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### Question 118
What is the ratio of the number of students in BCom third year to those in BSc second year?

Given:
1. Let the number of BCom first-year students be \( x \).
2. BCom third-year students are 25% less than BCom first-year students.

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###

In the year 2023, an undergraduate college had three courses - BA, BCom, and BSc. The course duration for all courses is 3 years. The ratio of the total number of students in all the years in BA, BCom, and BSc is 6:7:9 respectively. There are 1250 students in the first year, whereas those in the second year are 12% less. The difference between the total number of students in first and second year is the same as the difference between the total number of students in the second and third year. Various questions related to student distribution and calculations are posed based on these conditions.

Analyze student distribution across BA, BCom, and BSc courses with questions on ratios, percentages, and year-wise student count in 2023. This solution includes detailed calculations for complex academic scenarios suitable for entrance exam preparation.

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