A sum of money at simple interest amounts to Rs 500 in 2yr and Rs 900 in 4yr. That sum of money will be

Options

A. Rs 100
B. Rs 200
C. Rs 300
D. Rs 400

Answer

To solve the problem, we need to determine the principal amount (P) based on the information given about the amounts at different times.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The amount after 2 years (A1) is Rs 500.
- The amount after 4 years (A2) is Rs 900.

2. **Use the Simple Interest Formula:**
The formula for the amount in simple interest is:
\[ A = P + SI \]
where \( SI \) (Simple Interest) can be calculated as:
\[ SI = P \times r \times t \]
Here, \( r \) is the rate of interest and \( t \) is the time in years.

3. **Set Up the Equations:**
For 2 years:
\[ A_1 = P + SI_1 = P + P \times r \times 2 = 500 \]
For 4 years:
\[ A_2 = P + SI_2 = P + P \times r \times 4 = 900 \]

4. **Express the Simple Interest:**
From the first equation:
\[ SI_1 = P \times r \times 2 = 500 - P \]
From the second equation:
\[ SI_2 = P \times r \times 4 = 900 - P \]

5. **Find the Difference in Simple Interest:**
The difference in amounts after 4 years and 2 years gives us the interest earned in the additional 2 years:
\[ A_2 - A_1 = SI_2 - SI_1 \]
\[ 900 - 500 = (900 - P) - (500 - P) \]
\[ 400 = 400 \]

6. **Calculate the Simple Interest for 2 Years:**
We know that the interest earned in 2 years (SI for 2 years) is Rs 400:
\[ SI_1 = 500 - P \]
Thus,
\[ 400 = 500 - P \]
Rearranging gives:
\[ P = 500 - 400 = 100 \]

7. **Conclusion:**
The principal amount (P) is Rs 100.

### Final Answer:
The sum of money (principal) is Rs 100.