Rahul, Sandy, and Sati initially invested in the ratio 2 : 3 : 4. After 4 months, Sandy added Rs. 1500 to his investment, and Rahul withdrew Rs. 800 from his investment. After another 6 months, Sati added an amount equal to half of Rahul's initial 4-month investment, Sandy invested 50% more than Sati's total investment in the first 10 months, and Rahul added an amount equal to Sandy's investment in the first 4 months. The ratio of Sati's profit to the total profit at the end of the year is 125 : 376.

Veer has 250% more than Sati's initial investment and invests this amount in a scheme offering 20% per annum compound interest for 2 years. What is the total interest earned by Veer after 2 years?

Question

Rahul, Sandy, and Sati initially invested in the ratio 2 : 3 : 4. After 4 months, Sandy added Rs. 1500 to his investment, and Rahul withdrew Rs. 800 from his investment. After another 6 months, Sati added an amount equal to half of Rahul's initial 4-month investment, Sandy invested 50% more than Sati's total investment in the first 10 months, and Rahul added an amount equal to Sandy's investment in the first 4 months. The ratio of Sati's profit to the total profit at the end of the year is 125 : 376.

Veer has 250% more than Sati's initial investment and invests this amount in a scheme offering 20% per annum compound interest for 2 years. What is the total interest earned by Veer after 2 years?

Accepted Answer

**Solution:**

1. Let the initial investments of Rahul, Sandy, and Sati be Rs. 2x, Rs. 3x, and Rs. 4x respectively.

2. After 4 months:
   - Sandy adds Rs. 1500, so his investment becomes Rs. (3x + 1500).
   - Rahul withdraws Rs. 800, so his investment becomes Rs. (2x - 800).

3. After 6 more months (i.e., at 10 months):
   - Sati adds half of Rahul's initial 4-month investment: half of 2x = x.
     So, Sati's investment becomes Rs. (4x + x) = Rs. 5x.

- Sandy invests 50% more than Sati's total investment in first 10 months:
     Sati's total investment in first 10 months = Rs. 4x for 4 months + Rs. 5x for 6 months.

- Rahul adds an amount equal to Sandy's investment in first 4 months:
     Sandy's investment in first 4 months = Rs. 3x.

4. Using the profit ratio of Sati to total profit = 125 : 376, we can find the value of x and then Sati's initial investment.

5. Veer has 250% more than Sati's initial investment:
   - 250% more means Veer's investment = Sati's initial investment + 2.5 × Sati's initial investment = 3.5 × Sati's initial investment = 3.5 × 4x = 14x.

6. Veer invests Rs. 14x at 20% compound interest per annum for 2 years.

7. Compound interest formula:
   $$A = P 	imes \left(1 + \frac{r}{100}ight)^n$$
   Where,
   - $P = 14x$
   - $r = 20$
   - $n = 2$

8. Calculate amount:
   $$A = 14x 	imes (1.2)^2 = 14x 	imes 1.44 = 20.16x$$

9. Interest earned = $A - P = 20.16x - 14x = 6.16x$

10. From the profit ratio and investments, solving for $x$ gives $x = 250$.

11. Therefore, interest earned by Veer:
    $$6.16 	imes 250 = Rs. 1540$$

**Answer:** Rs. 1540

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