The simple interest on a sum of money will be ₹ 600 after 10 years. If the principal is trebled after 5 years, what will be the total interest at the end of the tenth year?

### Concept & Formula Simple interest accrues uniformly over time. Furthermore, simple interest is directly proportional to the principal. If the principal is multiplied by a factor, the interest generated for that period is multiplied by the same factor. $$SI \propto Principal$$ (when Rate and Time are constant) ### Step-by-Step Solution 1. **Given:** Total Simple Interest for 10 years on a normal principal = ₹ 600. 2. Since simple interest is uniform, the interest accrued over the first 5 years is exactly half of the 10-year interest. Interest for first 5 years = $\frac{600}{2} = 300$. 3. If the principal were unchanged, the interest for the next 5 years would also be ₹ 300. 4. However, the principal is trebled (multiplied by 3) after 5 years. 5. Because $SI$ is directly proportional to the Principal, the interest for the next 5 years will also be trebled. New interest for the last 5 years = $3 \times 300 = 900$. 6. Calculate total interest for the 10-year period: Total Interest = (Interest for first 5 years) + (New interest for last 5 years) Total Interest = $300 + 900 = 1200$. ### Exam Strategy & Shortcut Recognize the proportionality immediately. 10 years yields 600, so each 5-year block yields 300 on the base principal. The timeline is: [1 $\times$ Principal for 5 yrs] + [3 $\times$ Principal for 5 yrs]. Interest = $1 \times 300 + 3 \times 300 = 300 + 900 = 1200$. ### Common Pitfall A common mistake is choosing "Data inadequate" assuming you need the exact principal and rate to solve the problem. Proportionality principles make the absolute values unnecessary. ### Final Answer Therefore, the correct answer is **₹ 1200**.