To solve this problem, let's use the formula for simple interest:

$\text{Simple Interest} (SI) = \frac{P \times R \times T}{100}$

Where:

• $P$ is the principal amount,
• $R$ is the rate of interest (in % per annum),
• $T$ is the time (in years).

Given information:

• The simple interest is $\frac{1}{25}$ of the principal, i.e., $SI = \frac{P}{25}$,
• $R = T$ (rate and time are equal).

Now, substitute the given values into the simple interest formula:

$\frac{P \times R \times R}{100} = \frac{P}{25}$

Simplify the equation by canceling $P$ on both sides:

$\frac{R^2}{100} = \frac{1}{25}$

Multiply both sides by 100:

$R^2 = \frac{100}{25}$

$R^2 = 4$

Taking the square root of both sides:

$R = 2$

Thus, the rate of interest is 2%.

Final Answer:

The correct option is (a) 2%.

Would you like further details on this or have any questions?

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Here are 5 related questions:

1. What is the formula for compound interest?
2. How does simple interest differ from compound interest?
3. What happens if the time period is halved in simple interest calculations?
4. How can the rate of interest be determined if the principal and interest are known?
5. How does the principal change when the rate of interest increases?

Tip: In simple interest problems, always check if the rate and time are given in compatible units (years, months) to avoid errors.