An amount of Rs $P$ is invested in scheme A on compound interest at a rate of 20\% p.a. and the same amount is invested in scheme B on simple interest at a rate of 20\% p.a. At the end of two years, the difference between the interest received from both schemes is Rs 260.

**Quantity I:** If Rs $\frac{3P}{4}$ is invested at a rate of 6\% p.a. for four years in simple interest, then find the interest received.

**Quantity II:** Rs 1100

Compare Quantity I and Quantity II:

Question

An amount of Rs $P$ is invested in scheme A on compound interest at a rate of 20\% p.a. and the same amount is invested in scheme B on simple interest at a rate of 20\% p.a. At the end of two years, the difference between the interest received from both schemes is Rs 260.

**Quantity I:** If Rs $\frac{3P}{4}$ is invested at a rate of 6\% p.a. for four years in simple interest, then find the interest received.

**Quantity II:** Rs 1100

Compare Quantity I and Quantity II:

Accepted Answer

**Solution:**

1. Let the principal amount be $P$.

2. Scheme A: Compound Interest at 20\% p.a. for 2 years.
   - Compound Interest (CI) formula:
     $$\text{CI} = P \times \left(1 + \frac{r}{100}\right)^n - P$$
   - Here, $r = 20\%$, $n = 2$
   - Calculate CI:
     $$\text{CI} = P \times \left(1 + \frac{20}{100}\right)^2 - P = P \times (1.2)^2 - P = P \times 1.44 - P = 0.44P$$

3. Scheme B: Simple Interest at 20\% p.a. for 2 years.
   - Simple Interest (SI) formula:
     $$\text{SI} = \frac{P \times r \times t}{100}$$
   - Here, $r = 20\%$, $t = 2$
   - Calculate SI:
     $$\text{SI} = \frac{P \times 20 \times 2}{100} = 0.4P$$

4. Given the difference between interest from both schemes is Rs 260:
   $$\text{CI} - \text{SI} = 0.44P - 0.4P = 0.04P = 260$$

5. Solve for $P$:
   $$0.04P = 260 \implies P = \frac{260}{0.04} = 6500$$

6. Quantity I: Interest from Rs $\frac{3P}{4}$ at 6\% p.a. for 4 years (Simple Interest).
   - Principal = $\frac{3 \times 6500}{4} = 4875$
   - Rate = 6\%
   - Time = 4 years
   - Calculate SI:
     $$\text{SI} = \frac{4875 \times 6 \times 4}{100} = \frac{4875 \times 24}{100} = 1170$$

7. Quantity II = Rs 1100

8. Compare Quantity I and Quantity II:
   - Quantity I = Rs 1170
   - Quantity II = Rs 1100

9. Since $1170 > 1100$, Quantity I > Quantity II.

**Answer:** (a) Quantity I > Quantity II

**Note:** The correct answer is (a) based on calculations. However, the options marked above have (b) as correct, which is a mistake. The correct marking should be:

- (a) Quantity I > Quantity II — **True**
- Others — False

Please consider this correction.

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