In what time will a sum of Rs10,200 yield Rs13,005 as simple interest at the rate of 17% per annum?

Options

A. (A) 7 years 6 months
B. (B) 7 years 3 months
C. (C) 7 years 9 months
D. (D) 8 years

Answer

To solve the problem, we need to determine the time it takes for a principal amount of Rs. 10,200 to yield a simple interest of Rs. 13,005 at a rate of 17% per annum.

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = Rs. 10,200
- Simple Interest (SI) = Rs. 13,005
- Rate of Interest (R) = 17% per annum

2. **Use the formula for Simple Interest:**
\[ SI = \frac{P \times R \times T}{100} \]
where SI is the simple interest, P is the principal, R is the rate of interest, and T is the time in years.

3. **Rearrange the formula to solve for time (T):**
\[ T = \frac{SI \times 100}{P \times R} \]

4. **Substitute the known values into the formula:**
\[ T = \frac{13,005 \times 100}{10,200 \times 17} \]

5. **Calculate the denominator:**
\[ 10,200 \times 17 = 173,400 \]

6. **Calculate the time (T):**
\[ T = \frac{13,005 \times 100}{173,400} \]
\[ T = \frac{1,300,500}{173,400} \]

7. **Perform the division:**
\[ T \approx 7.5 \text{ years} \]

8. **Convert 0.5 years into months:**
\[ 0.5 \text{ years} = 6 \text{ months} \]

9. **Final answer:**
\[ T = 7 \text{ years and } 6 \text{ months} \]

### Conclusion:
The time required for the sum of Rs. 10,200 to yield Rs. 13,005 as simple interest at the rate of 17% per annum is **7 years and 6 months**.