To find out how many leaves the student can take in November while maintaining 75% attendance, we first need to determine the total number of school days and the required number of attended days for both November and December.

Step 1: Calculate Total Open Days

1. June: 5 days
2. July: Assume no school (0 days)
3. August: 21 days
4. September: 20 days
5. October: 21 days
6. November: 22 days
7. December: 15 days

Total open days from June to December: $5 + 0 + 21 + 20 + 21 + 22 + 15 = 104 \text{ days}$

Step 2: Calculate Total Attended Days

The student has 65% attendance up to the end of October, which means:

$\text{Total attended days} = 0.65 \times (\text{Total open days till October})$

Total open days till October: $5 + 0 + 21 + 20 + 21 = 67 \text{ days}$

Total attended days till October: $0.65 \times 67 = 43.55 \approx 44 \text{ days} \quad (\text{since days are whole, we round to nearest whole number})$

Leaves taken till October: $\text{Total leaves} = \text{Total open days till October} - \text{Total attended days}$ $= 67 - 44 = 23 \text{ leaves}$ (However, the problem states he has taken 20 leaves, so we will proceed with that.)

Step 3: Calculate Required Attendance for 75%

To maintain 75% attendance by the end of December, we calculate:

Total days required for 75% attendance: $0.75 \times 104 = 78 \text{ days}$

Current attendance days (up to October): 44 days

Step 4: Calculate Required Attended Days in November and December

Total additional days required to reach 78 days: $78 - 44 = 34 \text{ days}$

Total open days in November and December: $22 + 15 = 37 \text{ days}$

Step 5: Determine Leaves in November

Let $x$ be the number of leaves taken in November. Therefore, the attended days in November will be: $22 - x$ To achieve the required attendance: $(22 - x) + 15 \geq 34$ Solving for $x$: $22 - x + 15 \geq 34 \implies 37 - x \geq 34 \implies x \leq 3$

Conclusion

The student can take a maximum of 3 leaves in November while maintaining a minimum of 75% attendance by the end of December.

Summary

1. Total open days (June - December): 104 days
2. Required days attended for 75%: 78 days
3. Current attended days (up to October): 44 days
4. Additional days required: 34 days
5. Leaves allowed in November: 3

Would you like more details or clarification? Here are some questions for further exploration:

1. How would the attendance change if the student attended more days in October?
2. What are the implications of attendance on overall academic performance?
3. How can the student manage their time to avoid excessive absenteeism?
4. What strategies can students use to keep track of their attendance?
5. How does attendance policy vary among different schools?

Tip: Keeping a detailed attendance log can help students stay aware of their standing and make informed decisions about taking leaves.