The sum of money will amount to Rs. 900 in 4 yr at 5% per annum on simple interest is

Options

A. Rs. 1250
B. Rs. 900
C. Rs. 750
D. None of these

Answer

To find the principal amount (the sum of money) that will amount to Rs. 900 in 4 years at a simple interest rate of 5% per annum, we can use the formula for the amount in simple interest:

\[ A = P + SI \]

Where:
- \( A \) is the total amount after time \( t \)
- \( P \) is the principal amount (the sum of money we want to find)
- \( SI \) is the simple interest

The simple interest can be calculated using the formula:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( R \) is the rate of interest per annum
- \( T \) is the time in years

Given:
- \( A = 900 \)
- \( R = 5\% \)
- \( T = 4 \) years

### Step 1: Calculate the Simple Interest
Using the formula for simple interest:

\[ SI = \frac{P \times R \times T}{100} \]

Substituting the values we know:

\[ SI = \frac{P \times 5 \times 4}{100} = \frac{20P}{100} = \frac{P}{5} \]

### Step 2: Substitute SI in the Amount Formula
Now, we can substitute \( SI \) back into the amount formula:

\[ A = P + SI \]

This gives us:

\[ 900 = P + \frac{P}{5} \]

### Step 3: Combine the Terms
To combine the terms on the right side, we can express \( P \) as a fraction:

\[ 900 = P + \frac{P}{5} = \frac{5P + P}{5} = \frac{6P}{5} \]

### Step 4: Solve for P
Now, we can solve for \( P \):

\[ 900 = \frac{6P}{5} \]

To eliminate the fraction, multiply both sides by 5:

\[ 900 \times 5 = 6P \]

\[ 4500 = 6P \]

Now, divide both sides by 6:

\[ P = \frac{4500}{6} = 750 \]

### Conclusion
The sum of money (the principal amount) is Rs. 750.