The simple interest on a certain sum of money is Rs 600 after 10 years. If, after the first 5 years, the principal is trebled and the new larger principal is continued at the same rate of simple interest for the remaining 5 years, what will be the total simple interest earned at the end of 10 years?

Introduction / Context:
This question mixes a basic simple interest calculation with a change in principal partway through the total time period. First, you are told how much interest a certain sum earns in 10 years, which allows you to relate principal and rate. Then the question asks what happens if, after 5 years, the principal is trebled and the same rate is used for the remaining period. This tests your ability to use proportional reasoning and handle changes in principal over different intervals.

Given Data / Assumptions:

A sum of money earns simple interest of Rs 600 in 10 years.
Principal is P rupees and rate is r% per annum.
Simple interest formula: SI = (P * r * T) / 100.
After the first 5 years, the principal becomes 3P and the same rate r continues for the next 5 years.
Total time considered is 10 years (5 years + 5 years).

Concept / Approach:
From the original information, we know the interest on principal P for 10 years is Rs 600. That gives us a relation between P and r. Using proportionality of simple interest with respect to principal and time, we can then compute interest for P over 5 years and for 3P over 5 years, without explicitly finding r. Adding these two parts gives the total interest when the principal is trebled after 5 years.

Step-by-Step Solution:
Step 1: From the original condition, SI_original = 600 for 10 years on principal P at rate r. Step 2: Using SI = (P * r * T) / 100, 600 = (P * r * 10) / 100. Step 3: Rearranging, P * r = 600 * 100 / 10 = 6000. Step 4: Interest on P for the first 5 years: SI_first = (P * r * 5) / 100. Step 5: Since P * r = 6000, SI_first = (6000 * 5) / 100 = 30000 / 100 = 300. Step 6: After 5 years, principal becomes 3P, so interest for the next 5 years: SI_second = (3P * r * 5) / 100. Step 7: 3P * r = 3 * (P * r) = 3 * 6000 = 18000. Step 8: Thus, SI_second = (18000 * 5) / 100 = 90000 / 100 = 900. Step 9: Total interest with changed principal = SI_first + SI_second = 300 + 900 = 1200.

Verification / Alternative check:
A quick verification is to compute the average principal over each period and use proportionality. For the first 5 years, interest is 300, and for the next 5 years with triple principal, interest should be triple that of the first segment over equal time, that is 3 * 300 = 900. The sum 300 + 900 reproduces 1200, confirming the result.

Why Other Options Are Wrong:
Rs 1,100, Rs 1,000, Rs 1,840, and Rs 900 do not correctly reflect the proportional scaling of interest when principal is tripled for half the total time. They either underestimate or overestimate the contribution from the larger principal segment. Only Rs 1,200 matches the correctly computed total interest.

Common Pitfalls:
Learners sometimes mistakenly triple the entire 10-year interest or forget that the principal changes only after 5 years, not from the beginning. Another common error is to try to find the exact rate r unnecessarily, which can introduce arithmetic mistakes. It is often simpler to work with the product P * r, as shown in this solution.

Final Answer:
The total simple interest earned at the end of 10 years under the changed principal condition is Rs 1,200.