Arun invested Rs $x$ in Scheme I for 3 years at a simple interest rate of 12% per annum. Kush invested Rs $x + 4000$ in Scheme II for 2 years at a compound interest rate of 20% per annum. If the total interest earned by both Arun and Kush is Rs 3360, find the amount invested by Kush.

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Accepted Answer

**Solution:**

1. Let Arun's investment be Rs $x$.

2. Arun's interest from Scheme I (Simple Interest) for 3 years at 12% p.a.:
   $$
  $$ SI = \frac{P \times R \times T}{100} = \frac{x \times 12 \times 3}{100} = \frac{36x}{100} = 0.36x$$
   $$

3. Kush's investment is Rs $x + 4000$.

4. Kush's interest from Scheme II (Compound Interest) for 2 years at 20% p.a.:
   Compound amount after 2 years:
   $$
   $$A = P \times \left(1 + \frac{R}{100}\right)^T = (x + 4000) \times \left(1 + \frac{20}{100}\right)^2 = (x + 4000) \times (1.2)^2 = (x + 4000) \times 1.44$$
   $$

Compound interest earned by Kush:
   $$
   CI = A - P = 1.44(x + 4000) - (x + 4000) = 0.44(x + 4000)
   $$

5. Total interest earned by both is Rs 3360:
   $$
   0.36x + 0.44(x + 4000) = 3360
   $$

6. Simplify the equation:
   $$
   $0.36x + 0.44x + 0.44 \times 4000 = 3360$
   $$
   $$
   0.8x + 1760 = 3360
   $$
   $$
   0.8x = 3360 - 1760 = 1600
   $$
   $$
  $ x = \frac{1600}{0.8} = 2000$
   $$

7. Kush's investment:
   $$
   x + 4000 = 2000 + 4000 = 6000
   $$

**Answer:** Rs $6000$

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