In what time will Rs 8,000 at 3 % per annum, produces the same interset as Rs 6,000 does in 5 years at 4 % simple interset ?

Options

A. 5 years
B. 6 years
C. 3 years
D. 4 years

Answer

To solve the problem, we need to find the time it takes for Rs 8,000 at 3% per annum to produce the same interest as Rs 6,000 does in 5 years at 4% simple interest.

### Step-by-Step Solution:

1. **Calculate the Simple Interest (SI) for Rs 6,000 at 4% for 5 years:**
- Formula for Simple Interest:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, \( P = 6000 \), \( R = 4 \), and \( T = 5 \).
- Plugging in the values:
\[ SI_2 = \frac{6000 \times 4 \times 5}{100} \]
- Calculate:
\[ SI_2 = \frac{120000}{100} = 1200 \]

2. **Set up the equation for the Simple Interest for Rs 8,000 at 3%:**
- We need to find the time \( T \) when the interest produced by Rs 8,000 at 3% equals Rs 1,200 (the interest calculated in step 1).
- Using the same formula for Simple Interest:
\[ SI_1 = \frac{8000 \times 3 \times T}{100} \]
- We set \( SI_1 = SI_2 \):
\[ \frac{8000 \times 3 \times T}{100} = 1200 \]

3. **Solve for \( T \):**
- Rearranging the equation:
\[ 8000 \times 3 \times T = 1200 \times 100 \]
- Simplifying:
\[ 24000T = 120000 \]
- Dividing both sides by 24000:
\[ T = \frac{120000}{24000} = 5 \]

4. **Conclusion:**
- The time \( T \) required for Rs 8,000 at 3% per annum to produce the same interest as Rs 6,000 does in 5 years at 4% simple interest is **5 years**.