The sum which amounts to X 364.80 in 8 yr at 3.5% simple interest per annum is

Options

A. X 285
B. X 280
C. X 275
D. X 270

Answer

To solve the problem of finding the principal sum that amounts to ₹364.80 in 8 years at a simple interest rate of 3.5% per annum, we can follow these steps:

### Step 1: Understand the formula for Simple Interest
The formula for calculating the amount (A) using simple interest is:
\[ A = P + SI \]
Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (initial sum)
- \( SI \) = Simple Interest

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Set up the equation
From the problem, we know:
- \( A = 364.80 \)
- \( R = 3.5\% \)
- \( T = 8 \) years

Let the principal amount be \( P \). Therefore, we can express the total amount as:
\[ A = P + SI \]
Substituting the formula for SI, we get:
\[ 364.80 = P + \frac{P \times 3.5 \times 8}{100} \]

### Step 3: Simplify the equation
Now, we can simplify the equation:
1. Calculate the Simple Interest part:
\[ SI = \frac{P \times 3.5 \times 8}{100} = \frac{28P}{100} = \frac{7P}{25} \]

2. Substitute this back into the equation:
\[ 364.80 = P + \frac{7P}{25} \]

### Step 4: Combine like terms
To combine the terms on the right side, we need a common denominator:
\[ 364.80 = \frac{25P}{25} + \frac{7P}{25} \]
\[ 364.80 = \frac{25P + 7P}{25} \]
\[ 364.80 = \frac{32P}{25} \]

### Step 5: Solve for P
Now, we can solve for \( P \):
1. Multiply both sides by 25 to eliminate the fraction:
\[ 364.80 \times 25 = 32P \]
\[ 9120 = 32P \]

2. Divide both sides by 32:
\[ P = \frac{9120}{32} \]

3. Calculate:
\[ P = 285 \]

### Conclusion
The principal sum that amounts to ₹364.80 in 8 years at a simple interest rate of 3.5% per annum is **₹285**.

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