Simple interest on a certain sum of money "P" for 4 years at `5%` per annum is`50%` of the compound interest earned on Rs.3,000 for 2 years at `10%` per annum. The sum "P" placed on simple interest is:

Options

A. Rs.1,575
B. Rs.2,200
C. Rs.1,200
D. Rs.1,625

Answer

To solve the problem step by step, we will first calculate the compound interest on Rs. 3000 for 2 years at 10% per annum, and then use that information to find the sum "P" for which the simple interest for 4 years at 5% per annum is 50% of the compound interest calculated.

### Step 1: Calculate the Compound Interest (CI) on Rs. 3000 for 2 years at 10% per annum.

1. **Formula for Compound Interest:**
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount (Rs. 3000)
- \( r \) = Rate of interest (10%)
- \( t \) = Time (2 years)

2. **Substituting the values:**
\[ A = 3000 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 3000 \left(1 + 0.1\right)^2 = 3000 \left(1.1\right)^2 \]
\[ A = 3000 \times 1.21 = 3630 \]

3. **Calculate the Compound Interest (CI):**
\[ CI = A - P = 3630 - 3000 = 630 \]

### Step 2: Find the Simple Interest (SI) which is 50% of the Compound Interest.

1. **Calculate 50% of CI:**
\[ SI = \frac{50}{100} \times CI = \frac{50}{100} \times 630 = 315 \]

### Step 3: Use the Simple Interest to find the sum "P".

1. **Formula for Simple Interest:**
\[ SI = \frac{P \times r \times t}{100} \]
where:
- \( SI = 315 \)
- \( r = 5\% \)
- \( t = 4 \) years

2. **Substituting the values:**
\[ 315 = \frac{P \times 5 \times 4}{100} \]
\[ 315 = \frac{20P}{100} \]
\[ 315 = \frac{P}{5} \]

3. **Solving for \( P \):**
\[ P = 315 \times 5 = 1575 \]

### Conclusion:
The sum "P" placed on simple interest is Rs. 1575.

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