Mr. Dua invested money in two schemes A and B offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a. respectively. If the total amount of interest accrued through two schemes together in two years was ₹ 4818.30 and the total amount invested was ₹ 27,000, what was the amount invested in Scheme A?

### Concept & Compound Interest on Multiple Schemes When a total sum is split into two different investment schemes, we can set up an algebraic equation based on the effective interest rates for each scheme over the given time period. $$Effective\ Rate = A + B + \frac{A \times B}{100}$$ ### Step-by-Step Solution 1. **Define the variables:** Let the amount invested in Scheme A be $x$. Then, the amount invested in Scheme B is $(27000 - x)$. 2. **Calculate effective interest rates for 2 years:** Scheme A (8% p.a.): $8 + 8 + \frac{8 \times 8}{100} = 16.64\%$ Scheme B (9% p.a.): $9 + 9 + \frac{9 \times 9}{100} = 18.81\%$ 3. **Formulate the equation:** Total interest = Interest from A + Interest from B $4818.30 = 16.64\% \text{ of } x + 18.81\% \text{ of } (27000 - x)$ $4818.30 = 0.1664x + 0.1881(27000 - x)$ 4. **Solve for $x$:** $4818.30 = 0.1664x + 5078.7 - 0.1881x$ $0.1881x - 0.1664x = 5078.7 - 4818.30$ $0.0217x = 260.4$ $x = \frac{260.4}{0.0217} = \frac{2604000}{217} = 12000$ ### Exam Strategy & Shortcut You can use the method of alligation by finding the overall effective interest rate, but dealing with decimals like $17.845\%$ can be tedious. Using the effective rate equation directly is often safer and just as fast if you are comfortable with decimal multiplication. ### Common Pitfall A common mistake is using the Simple Interest formula instead of Compound Interest for the 2-year period, which drastically alters the interest percentages. ### Final Answer Therefore, the correct answer is **₹ 12,000**.