Abhishek borrowed Rs.1,20,000 from a bank at an 8\% compound interest rate for 2 years. He invested $\frac{3}{4}$ of this loan in a scheme offering 10\% compound interest annually for 2 years. He kept the remaining amount without investing. Calculate Abhishek's net profit or loss after 2 years.

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**Solution:**

1. **Calculate the compound amount for the loan:**
   - Principal $P = 1,20,000$
   - Rate $r = 8\%$ per annum
   - Time $t = 2$ years

Compound amount $$A = P \times \left(1 + \frac{r}{100}\right)^t = 1,20,000 \times \left(1 + \frac{8}{100}\right)^2$$

$$ $A = 1,20,000 \times (1.08)^2 = 1,20,000 \times 1.1664 = 1,39,968 $$$

2. **Calculate the invested amount and the remaining amount:**
   - Invested amount = $$\frac{3}{4} \times 1,20,000 = 90,000$$
   - Remaining amount = $1,20,000 - 90,000 = 30,000$

3. **Calculate the compound amount from the investment scheme:**
   - Principal $= 90,000$
   - Rate $= 10\%$
   - Time $= 2$ years

Compound amount $$= 90,000 \times (1 + \frac{10}{100})^2 = 90,000 \times (1.1)^2 = 90,000 \times 1.21 = 1,08,900$$

4. **Calculate total amount Abhishek has after 2 years:**
   - Total amount = Amount from investment + Remaining amount
   - $= 1,08,900 + 30,000 = 1,38,900$

5. **Calculate profit or loss:**
   - Amount owed to bank = Rs.1,39,968
   - Amount Abhishek has = Rs.1,38,900
   - Loss = $1,39,968 - 1,38,900 = 1,068$

**Answer:** Rs.1068 loss

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