A sum fetched a total simple interest of Rs.1,858.40 at the rate of `8% p.(a)` in 5 years. What is the sum?

Options

A. Rs.4,646
B. Rs.2,446
C. Rs.5,112
D. Rs.2,706

Answer

To find the principal sum (P) that fetched a total simple interest of Rs. 1858.40 at a rate of 8% per annum over 5 years, we can use the formula for simple interest:

**Simple Interest (SI) = (P × R × T) / 100**

Where:
- SI = Simple Interest
- P = Principal amount (the sum we want to find)
- R = Rate of interest (in percentage)
- T = Time (in years)

### Step-by-Step Solution:

1. **Identify the given values:**
- Simple Interest (SI) = Rs. 1858.40
- Rate (R) = 8%
- Time (T) = 5 years

2. **Substitute the values into the formula:**
\[ 1858.40 = \frac{P \times 8 \times 5}{100} \]

3. **Simplify the equation:**
- First, calculate \(8 \times 5 = 40\).
- Now the equation becomes:
\[ 1858.40 = \frac{P \times 40}{100} \]

4. **Multiply both sides by 100 to eliminate the fraction:**
\[ 185840 = P \times 40 \]

5. **Now, divide both sides by 40 to isolate P:**
\[ P = \frac{185840}{40} \]

6. **Calculate the value of P:**
\[ P = 4646 \]

Thus, the principal sum is **Rs. 4646**.

### Final Answer:
The sum is Rs. 4646.

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