Simple interest on a certain unknown sum of money for 3 years at 8% per annum is equal to half of the compound interest on Rs. 1200 for 2 years at 10% per annum. Find the principal that was placed on simple interest.

Introduction / Context:
This problem compares simple interest on one unknown sum with compound interest on a known sum at different rates. The condition given is that simple interest for 3 years at 8 percent per annum equals half of the compound interest on Rs. 1200 for 2 years at 10 percent per annum. Such mixed interest questions test understanding of both simple and compound interest formulas and the ability to link them through an equation.

Given Data / Assumptions:
For the compound interest part, principal is Rs. 1200, rate is 10 percent per annum, time is 2 years, and interest is compounded annually.
For the simple interest part, rate is 8 percent per annum, time is 3 years, and principal is unknown.
Simple interest on the unknown principal equals half of the compound interest on Rs. 1200.
All calculations use standard formulas for simple and compound interest.

Concept / Approach:
For compound interest, we use A = P * (1 + r / 100)^n and CI = A - P. First, we calculate compound interest on Rs. 1200 at 10 percent for 2 years. Then we take half of that value because the problem states that simple interest is equal to half of the compound interest. For simple interest, I = P * r * t / 100. We equate this simple interest expression to half of the compound interest and solve for the unknown principal.

Step-by-Step Solution:
Compute compound interest on Rs. 1200 at 10 percent per annum for 2 years.Amount A = 1200 * (1 + 10 / 100)^2 = 1200 * (1.1)^2.Calculate (1.1)^2 = 1.21, so A = 1200 * 1.21 = 1452 rupees.Compound interest CI = A - P = 1452 - 1200 = 252 rupees.Half of this compound interest is 252 / 2 = 126 rupees.Let the principal on simple interest be P rupees.Simple interest for 3 years at 8 percent per annum is I = P * 8 * 3 / 100 = 0.24P.Set this equal to 126: 0.24P = 126.Solve for P: P = 126 / 0.24 = 525 rupees.Therefore, the sum placed on simple interest is Rs. 525.

Verification / Alternative check:
Check simple interest on Rs. 525 at 8 percent for 3 years. I = 525 * 8 * 3 / 100 = 525 * 24 / 100 = 126 rupees. Earlier, we found that half of the compound interest on Rs. 1200 is exactly 126 rupees. Since the simple interest computed here matches half of that compound interest, the relationship in the question is satisfied, confirming our solution.

Why Other Options Are Wrong:
If P were 1050 rupees, simple interest would be 1050 * 8 * 3 / 100 = 252 rupees, which equals the full compound interest, not half of it.
For Rs. 260 or Rs. 420, the resulting simple interest would be much smaller than 126 rupees.
Rs. 630 as principal would produce simple interest greater than 126 rupees. Therefore none of these options meet the half equality condition.

Common Pitfalls:
Common errors include forgetting to subtract the principal when computing compound interest, incorrectly squaring 1.1, or misinterpreting half of compound interest as twice the simple interest. Some learners may accidentally equate simple interest to the full compound interest instead of half. Keeping track of each step and the exact relationship described in the problem prevents such mistakes.

Final Answer:
The principal placed on simple interest is Rs. 525.