What sum will fetch a simple interest of ₹ 25,410 in five and a half years at 6% p.a.rate of interest?

Options

A. ₹77,000
B. ₹88,000
C. ₹70,000
D. ₹55,000

Answer

To find the principal sum that will fetch a simple interest of ₹25,410 in five and a half years at a rate of 6% per annum, we can use the formula for simple interest:

**Simple Interest (SI) = (Principal (P) × Rate (R) × Time (T)) / 100**

### Step-by-Step Solution:

1. **Identify the given values:**
- Simple Interest (SI) = ₹25,410
- Rate (R) = 6% per annum
- Time (T) = 5.5 years (which can also be expressed as \( \frac{11}{2} \) years)

2. **Substitute the values into the formula:**
\[ 25410 = \frac{P \times 6 \times \frac{11}{2}}{100} \]

3. **Simplify the equation:**
- First, multiply both sides by 100 to eliminate the fraction:
\[ 25410 \times 100 = P \times 6 \times \frac{11}{2} \]
- This simplifies to:
\[ 2541000 = P \times 6 \times \frac{11}{2} \]

4. **Calculate \( 6 \times \frac{11}{2} \):**
\[ 6 \times \frac{11}{2} = \frac{66}{2} = 33 \]

5. **Now, substitute back into the equation:**
\[ 2541000 = P \times 33 \]

6. **Solve for P:**
\[ P = \frac{2541000}{33} \]

7. **Calculate the value of P:**
- Dividing:
\[ P = 77000 \]

### Final Answer:
The principal sum that will fetch a simple interest of ₹25,410 in five and a half years at a rate of 6% per annum is **₹77,000**.