If the ratio of principal amount and simple interest of one year is 25 : 1, then rate of interest is :

Question

Accepted Answer

To determine the rate of interest when the ratio of the principal amount to the simple interest for one year is 25:1, we can use the formula for simple interest:

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

Given that the time (T) is 1 year, the formula simplifies to:

$$ \text{SI} = \frac{P \times R}{100} $$

According to the problem, the ratio of the principal amount to the simple interest is 25:1. This means:

$$ \frac{P}{SI} = 25 $$

Substituting the expression for SI from the formula:

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

Simplifying the equation:

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

Solving for R:

$$ R = \frac{100}{25} = 4\% $$

Therefore, the rate of interest is 4%, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (25%)**: If the rate were 25%, the ratio of principal to simple interest would not be 25:1. Instead, it would be 4:1, as calculated by substituting 25% into the formula, which contradicts the given ratio.

- **Option 3 (5%)**: If the rate were 5%, the ratio of principal to simple interest would be 20:1, not 25:1. This does not match the given condition.

- **Option 4 (20%)**: If the rate were 20%, the ratio of principal to simple interest would be 5:1, which again does not satisfy the condition of a 25:1 ratio.

Thus, the only rate that satisfies the condition of a 25:1 ratio of principal to simple interest is 4%, making Option 1 the correct answer.