Anurag and Ravi started a business with capitals of Rs. 2000 and Rs. 1600 respectively. After 8 months, Anurag added Rs. 400 more to his capital and then left the business after 10 months. At the end of one year, Ravi invested his profit in a scheme offering compound interest at 20% per annum. If after two years, Ravi receives a total amount of Rs. 6912 from this investment, what is the total profit earned by Anurag?

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**Solution:**

1. **Calculate Ravi's profit:**
   - Ravi invested his profit in a scheme with compound interest (CI) at 20% per annum.
   - After 2 years, the amount Ravi received is Rs. 6912.

2. **Find the principal (profit) Ravi invested:**
   - Using compound interest formula:
     $$A = P 	imes \left(1 + \frac{r}{100}ight)^t$$
     where,
     - $A = 6912$
     - $r = 20\%$
     - $t = 2$ years

- Substitute values:
     $$6912 = P 	imes (1 + 0.20)^2 = P 	imes (1.44)$$

- Calculate $P$:
     $$P = \frac{6912}{1.44} = 4800$$

So, Ravi's profit = Rs. 4800.

3. **Calculate the ratio of capitals considering time:**
   - Anurag's capital:
     - For first 8 months: Rs. 2000
     - For next 2 months: Rs. 2000 + Rs. 400 = Rs. 2400
     - Total capital contribution in terms of month-capital:
       $$2000 	imes 8 + 2400 	imes 2 = 16000 + 4800 = 20800$$

- Ravi's capital for 12 months:
     $$1600 	imes 12 = 19200$$

4. **Profit sharing ratio:**
   $$	ext{Anurag} : 	ext{Ravi} = 20800 : 19200 = 13 : 12$$

5. **Calculate Anurag's profit:**
   - Total profit = Anurag's profit + Ravi's profit
   - Let total profit be $x$.
   - Using ratio:
     $$\frac{	ext{Anurag's profit}}{	ext{Ravi's profit}} = \frac{13}{12}$$

- Since Ravi's profit = 4800,
     $$	ext{Anurag's profit} = \frac{13}{12} 	imes 4800 = 5200$$

6. **Check total profit:**
   $$5200 + 4800 = 10000$$

**Answer:** Rs. 5200

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