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The question in Gujarati asks for the calculation of the principal sum (કેટલું મૂલ્ય) based on given compound interest values over different time periods.

### Translation and Interpretation:
Let:
- \( P \) = Principal amount (the amount we need to find).
- Compound interest after 3 years = ₹ 4000.
- Compound interest after 6 years = ₹ 9600.

We are asked to find the principal \( P \).

Since we are given the compound interest values at two different time intervals, we can solve this using the concept of compound interest growth over equal periods.

---

### Solution:
In compound interest problems, if the interest compounds annually at a constant rate, we know:
\[
A = P(1 + r)^n
\]
where:
- \( A \) is the amount after \( n \) years,
- \( r \) is the rate of interest.

Given the two compound interest values:
1. After 3 years, Compound Interest (CI) is ₹ 4000.
2. After 6 years, Compound Interest (CI) is ₹ 9600.

Let me calculate it based on this method.The solution yields the following results:

- The rate of interest \( r \) is approximately 33.89%.
- The principal amount \( P \), or the original sum, is approximately ₹ 2857.14.

### Summary:
The original principal amount is **₹ 2857.14**.

Would you like a detailed explanation on how these calculations were made? 

Here are five related questions to expand your understanding:

1. How does compound interest differ from simple interest?
2. How would the calculation change if the interest compounded quarterly instead of annually?
3. What would happen to the principal amount if the interest rate were lower?
4. How can we verify the principal amount using alternative methods?
5. How is the rate of interest derived from different periods of compound interest?

#### Tip:
In compound interest problems, knowing the interest over equal time periods can help deduce the rate of growth. This can simplify complex calculations for multi-year investments.

અમુક ચોક્કસ રકમ પર મળતું 3 વર્ષે ચકવૃદ્ધિ વ્યાજ 4000 તથા તે જ રકમ પર મળતું 6 વર્ષે ચકવૃદ્ધિ વ્યાજ 9600 હોય તો તે રકમ જણાવવો?

Learn how to determine the principal amount when given compound interest values of ₹4000 after 3 years and ₹9600 after 6 years. This solution explains key concepts of compound interest and exponential growth. Suitable for students in Grades 10-12.

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