The simple interest on a sum of money at 10% per annum for 6 yr is half the sum. Then, the sum is

Options

A. Rs. 5000
B. not possible
C. Rs. 4000
D. Rs. 6000

Answer

To solve the problem, we need to find the sum of money (principal amount, P) based on the information given about the simple interest.

### Step-by-step Solution:

1. **Understand the Given Information:**
We know that the simple interest (SI) earned on a sum of money at 10% per annum for 6 years is half of the principal amount (P).

2. **Write the Formula for Simple Interest:**
The formula for simple interest is:
\[ \text{SI} = \frac{P \times r \times t}{100} \]
where:
- \( P \) = principal amount
- \( r \) = rate of interest (in percentage)
- \( t \) = time (in years)

3. **Substitute the Known Values:**
From the problem, we have:
- \( r = 10\% \)
- \( t = 6 \) years
- SI = \(\frac{1}{2} P\)

Substituting these values into the formula gives:
\[ \frac{1}{2} P = \frac{P \times 10 \times 6}{100} \]

4. **Simplify the Equation:**
First, simplify the right side:
\[ \frac{1}{2} P = \frac{60P}{100} \]
This simplifies to:
\[ \frac{1}{2} P = \frac{3P}{5} \]

5. **Eliminate P from Both Sides:**
Since \( P \) is common on both sides, we can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ \frac{1}{2} = \frac{3}{5} \]

6. **Cross-Multiply to Solve for P:**
Cross-multiplying gives:
\[ 5 \cdot 1 = 2 \cdot 3 \]
Which simplifies to:
\[ 5 = 6 \]
This is a contradiction, indicating that our assumption leads to an impossible situation.

7. **Conclusion:**
Therefore, there does not exist any value of \( P \) that satisfies the given conditions.