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The image provided presents a mathematical problem in Hindi regarding compound interest. The question asks for the minimum time required for a certain amount of money to triple itself at a compound interest rate of 25%.

### Problem Breakdown:
- **Interest Rate**: 25% per annum
- **Objective**: Find the minimum number of years required for the initial amount to triple itself.

### Solution:
To solve this, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{100}\right)^n
\]

Where:
- \( A \) is the final amount (which is 3 times the principal \( P \), so \( A = 3P \)),
- \( P \) is the principal amount,
- \( r \) is the annual interest rate (25% in this case),
- \( n \) is the number of years.

So,

\[
3P = P \left(1 + \frac{25}{100}\right)^n
\]

This simplifies to:

\[
3 = \left(1.25\right)^n
\]

Now, to solve for \( n \), we can take the logarithm of both sides:

\[
\log(3) = n \cdot \log(1.25)
\]

\[
n = \frac{\log(3)}{\log(1.25)}
\]

Let's calculate this value:

\[
\log(3) \approx 0.4771
\]
\[
\log(1.25) \approx 0.0969
\]

So,

\[
n = \frac{0.4771}{0.0969} \approx 4.92
\]

Since the problem asks for the minimum time in whole years, we round up to the nearest whole number, giving \( n = 5 \) years.

### Conclusion:
The correct answer is **(d) 5 years**.

---

Do you want further details or have any questions?

Here are 5 related questions you could explore:
1. How would the result change if the interest rate were 20%?
2. What if the goal was to quadruple the amount? How many years would that take?
3. How is the compound interest formula different from the simple interest formula?
4. What role does the logarithm play in solving this type of problem?
5. How would you calculate the time if the interest was compounded semi-annually?

**Tip**: Always round up when calculating the minimum time required to achieve a certain growth in compound interest problems!

वह न्यूनतम समय जिसमें कुछ राशि चक्रवृद्धि ब्याज की 25% दर पर स्वयं की तीन गुनी हो जाएगी:

Learn how to calculate the minimum number of years required for an amount to triple itself at a compound interest rate of 25%. This problem involves key mathematical concepts like exponential growth, logarithms, and the compound interest formula. Suitable for Grades 10-12.

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