What sum will yield an interest of Rs. 7840 in 2 years at `6""1/4%` per annum?

Answer

To solve the problem, we need to find the principal amount (P) that will yield an interest of Rs. 7840 in 2 years at a rate of 6 1/4% per annum.

### Step-by-Step Solution:

1. **Identify the given values:**
- Simple Interest (SI) = Rs. 7840
- Time (T) = 2 years
- Rate (R) = 6 1/4% = 6.25%

2. **Convert the rate into a fraction:**
- 6 1/4% can be converted to an improper fraction:
\[ 6 \frac{1}{4} = \frac{25}{4} \text{ percent} \]

3. **Use the Simple Interest formula:**
- The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, we need to rearrange the formula to find P:
\[ P = \frac{SI \times 100}{R \times T} \]

4. **Substitute the known values into the formula:**
- Substitute SI = 7840, R = \frac{25}{4}, and T = 2 into the rearranged formula:
\[ P = \frac{7840 \times 100}{\left(\frac{25}{4}\right) \times 2} \]

5. **Calculate the denominator:**
- First, calculate \( \frac{25}{4} \times 2 \):
\[ \frac{25 \times 2}{4} = \frac{50}{4} = 12.5 \]

6. **Now substitute back to find P:**
- Substitute the value of the denominator back into the equation for P:
\[ P = \frac{7840 \times 100}{12.5} \]

7. **Perform the multiplication:**
- Calculate \( 7840 \times 100 = 784000 \)

8. **Finally, divide to find P:**
- Now divide \( 784000 \) by \( 12.5 \):
\[ P = \frac{784000}{12.5} = 62720 \]

9. **Conclusion:**
- The principal amount (P) is Rs. 62720.

### Final Answer:
The sum that will yield an interest of Rs. 7840 in 2 years at 6 1/4% per annum is **Rs. 62720**.