What sum will amount to Rs. 1292 in 3 years at 12% per annum simple interest?

Answer

To find the principal amount (P) that will amount to Rs. 1292 in 3 years at a simple interest rate of 12% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Amount**:
The formula for the amount (A) in simple interest is given by:
\[ A = P + SI \]
where \( SI \) (Simple Interest) is calculated as:
\[ SI = \frac{P \times R \times T}{100} \]
Here, \( R \) is the rate of interest and \( T \) is the time in years.

2. **Identify the Given Values**:
- Amount (A) = Rs. 1292
- Rate of Interest (R) = 12%
- Time (T) = 3 years

3. **Calculate Simple Interest**:
Substitute the values into the simple interest formula:
\[ SI = \frac{P \times 12 \times 3}{100} \]
Simplifying this gives:
\[ SI = \frac{36P}{100} = \frac{9P}{25} \]

4. **Substitute SI into the Amount Formula**:
Now substitute \( SI \) back into the amount formula:
\[ A = P + SI \]
This becomes:
\[ 1292 = P + \frac{9P}{25} \]

5. **Combine Like Terms**:
To combine \( P \) and \( \frac{9P}{25} \), we need a common denominator:
\[ P = \frac{25P}{25} \]
Thus:
\[ 1292 = \frac{25P}{25} + \frac{9P}{25} = \frac{34P}{25} \]

6. **Solve for P**:
Now, multiply both sides by 25 to eliminate the fraction:
\[ 1292 \times 25 = 34P \]
Calculate \( 1292 \times 25 \):
\[ 32300 = 34P \]
Now, divide both sides by 34:
\[ P = \frac{32300}{34} = 950 \]

7. **Final Answer**:
Therefore, the principal amount (P) that will amount to Rs. 1292 in 3 years at 12% per annum simple interest is:
\[ P = Rs. 950 \]