A certain sum of money amounts to Rs 15900 at simple rate of interest at 6% p.a in 1 years . What is the value of principal sum ?

Options

A. 12000
B. 18000
C. 15000
D. 1400

Answer

To find the principal sum when a certain amount is given at simple interest, we can use the formula for simple interest:

\[ A = P + SI \]

Where:
- \( A \) is the total amount after interest,
- \( P \) is the principal amount (the initial sum of money),
- \( SI \) is the simple interest.

The formula for simple interest is:

\[ SI = \frac{P \times r \times t}{100} \]

Where:
- \( r \) is the rate of interest,
- \( t \) is the time in years.

### Step-by-Step Solution:

1. **Identify the values given in the question:**
- Total amount \( A = 15900 \)
- Rate of interest \( r = 6\% \)
- Time \( t = 1 \) year

2. **Calculate the simple interest (SI):**
Using the formula for simple interest:
\[ SI = \frac{P \times r \times t}{100} \]
We need to express \( SI \) in terms of \( P \):
\[ SI = \frac{P \times 6 \times 1}{100} = \frac{6P}{100} = 0.06P \]

3. **Substitute the value of SI back into the total amount formula:**
\[ A = P + SI \]
Substituting the value of \( SI \):
\[ 15900 = P + 0.06P \]

4. **Combine like terms:**
\[ 15900 = P(1 + 0.06) = P(1.06) \]

5. **Solve for \( P \):**
\[ P = \frac{15900}{1.06} \]
\[ P = 15000 \]

### Conclusion:
The principal sum is Rs 15,000.