Quantity I : Amount obtained after two years on Rs. 2450 at ` 14 (2)/(7) % ` simple interest per annum
Quantity II : Amount obtained after two years on investment of Rs 2450 at ` 12 (1)/(2)` % p.a. compounded yearly

Options

A. Quantity I ` gt` Quantity II
B. Quantity I ` lt` Quantity II
C. Quantity I ` ge` Quantity II
D. Quantity I = Quantity II or no relation

Answer

To solve the problem, we need to calculate the amounts for both Quantity I (simple interest) and Quantity II (compound interest) based on the given rates and principal amount.

### Step-by-Step Solution

**Quantity I: Simple Interest Calculation**

1. **Identify the given values:**
- Principal (P) = Rs. 2450
- Rate of Interest (R) = 14 (2/7)% = 14.2857% (approximately)
- Time (T) = 2 years

2. **Convert the rate of interest into a fraction:**
- \( R = \frac{100}{7} \) (since 14 (2/7) = 14 + 2/7 = 14.2857)

3. **Calculate Simple Interest (SI):**
\[ SI = \frac{P \times R \times T}{100} = \frac{2450 \times \frac{100}{7} \times 2}{100} \]
\[ SI = \frac{2450 \times 2}{7} = \frac{4900}{7} = 700 \]

4. **Calculate the total amount after 2 years:**
\[ \text{Total Amount} = P + SI = 2450 + 700 = 3150 \]

**Quantity I Amount: Rs. 3150**

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**Quantity II: Compound Interest Calculation**

1. **Identify the given values:**
- Principal (P) = Rs. 2450
- Rate of Interest (R) = 12 (1/2)% = 12.5% = \( \frac{25}{200} = \frac{1}{8} \)
- Time (T) = 2 years

2. **Use the compound interest formula:**
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
\[ A = 2450 \left(1 + \frac{12.5}{100}\right)^2 = 2450 \left(1 + 0.125\right)^2 = 2450 \left(1.125\right)^2 \]

3. **Calculate \( (1.125)^2 \):**
\[ (1.125)^2 = 1.265625 \]

4. **Calculate the total amount:**
\[ A = 2450 \times 1.265625 \approx 3109.0625 \]

**Quantity II Amount: Rs. 3109.06 (approximately)**

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### Final Comparison

- Quantity I = Rs. 3150
- Quantity II = Rs. 3109.06

**Conclusion:** Quantity I is greater than Quantity II.