The uploaded image contains a set of compound interest (CI) and related problems written in both English and Nepali. Let’s address the mathematical content, providing solutions or explanations for some of the highlighted problems.

Problem Breakdown:

8A:

• Given: Principal $P = 5000$, Compound Amount (CA) after 3 years = $8500$.

• Find: Compound Interest (CI).

  Solution: $\text{CI} = \text{CA} - P$ Substituting the values: $\text{CI} = 8500 - 5000 = 3500$

8B:

• Given: Principal $P = 8000$, Compound Interest $\text{CI} = 3000$.

• Find: Compound Amount (CA).

  Solution: $\text{CA} = P + \text{CI}$ Substituting the values: $\text{CA} = 8000 + 3000 = 11000$

9A:

• Given: Compound Interest $\text{CI} = 8000$, Compound Amount $\text{CA} = 5000$.

• Find: Principal $P$.

  Solution: Using the relationship: $\text{CA} = P + \text{CI}$ Rearranging for $P$: $P = \text{CA} - \text{CI}$ Substituting: $P = 5000 - 8000 = -3000$ The question might have a mistake as this result seems invalid—double-check the values or clarify.

10A:

• Given: Principal = 4 times the Compound Interest $(\text{CI})$.

• Find: The relationship between $P$ and $\text{CI}$.

  Solution: If $P = 4 \times \text{CI}$, then: $P = 4 \, \text{CI} \quad \implies \quad \text{CI} = \frac{P}{4}$

10B:

• Given: Principal $P$ = one-third the Compound Interest $(\text{CI})$.

• Find: The relationship between $P$ and $\text{CI}$.

  Solution: If $P = \frac{1}{3} \, \text{CI}$, then: $\text{CI} = 3P$

Would you like me to work on any specific question in detail or move to different examples? Let me know!

Questions to Expand Understanding:

1. How is the compound amount formula derived from compound interest basics?
2. How does the time period affect the compound interest in real-life applications?
3. What is the difference between simple interest and compound interest calculations?
4. Why does compounding frequency (e.g., annually, semi-annually) affect the result?
5. Can we solve these problems using logarithms for a quicker approach?

Tip:

Always identify whether the problem involves compound interest or simple interest, as they follow different growth patterns and formulas.