If the ratio of principal and the simple interest for 5 years is 10 : 3, then the rate of interest is :

Options

A. 0.05
B. 0.06
C. 0.08
D. 0.03

Answer

To solve the problem, we need to find the rate of interest given the ratio of principal to simple interest over 5 years. Let's break it down step by step.

### Step 1: Understand the given ratio
We are given that the ratio of principal (P) to simple interest (SI) for 5 years is 10:3. This means:
\[ \frac{P}{SI} = \frac{10}{3} \]

### Step 2: Express SI in terms of P
From the ratio, we can express the simple interest (SI) in terms of principal (P):
\[ SI = \frac{3}{10} P \]

### Step 3: Use the formula for Simple Interest
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest (in percentage)
- T = Time (in years)

Given that the time (T) is 5 years, we can substitute this into the formula:
\[ SI = \frac{P \times R \times 5}{100} \]

### Step 4: Set the two expressions for SI equal
Now, we can set the two expressions for SI equal to each other:
\[ \frac{3}{10} P = \frac{P \times R \times 5}{100} \]

### Step 5: Simplify the equation
We can cancel P from both sides (assuming P ≠ 0):
\[ \frac{3}{10} = \frac{R \times 5}{100} \]

### Step 6: Cross-multiply to solve for R
Cross-multiplying gives us:
\[ 3 \times 100 = 10 \times R \times 5 \]
\[ 300 = 50R \]

### Step 7: Solve for R
Now, divide both sides by 50 to find R:
\[ R = \frac{300}{50} = 6 \]

### Conclusion
The rate of interest is:
\[ \boxed{6\%} \]

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