A person takes a loan of Rs. 200 at 5% per annum simple interest. He returns Rs. 100 at the end of 1 year. How much must he pay at the end of 2 years in order to clear all his dues?

Introduction / Context:
This question involves simple interest with a part payment made before the full term of the loan is completed. It tests whether you can correctly compute interest for different periods and adjust the outstanding principal after an interim payment. Such problems are common in bank related aptitude questions.

Given Data / Assumptions:

• Original loan (principal) = Rs. 200
• Rate of simple interest = 5% per annum
• Time from start to final settlement = 2 years
• Payment of Rs. 100 is made at the end of 1 year
• We assume that interest is calculated yearly on the outstanding principal

Concept / Approach:
Under simple interest, interest for each year is calculated on the principal that is outstanding during that year. A standard exam method is to treat the first year with the full principal and the second year with the reduced principal after the interim payment. Total interest over 2 years is then added to the total principal that has not yet been repaid to get the final payment amount.

Step-by-Step Solution:
Year 1: Principal = Rs. 200Interest for first year = (200 * 5 * 1) / 100 = Rs. 10At the end of year 1, he pays Rs. 100Total due at that moment (principal plus interest) can be viewed in a simplified way: we treat Rs. 100 as reducing the principal for the remaining periodFor year 2, we consider the outstanding principal for interest as Rs. 100Interest for second year = (100 * 5 * 1) / 100 = Rs. 5Total interest over 2 years = 10 + 5 = Rs. 15Total principal originally borrowed = Rs. 200He has already repaid Rs. 100 at the end of year 1So principal still to be repaid at the end of year 2 = 200 - 100 = Rs. 100Final payment at end of year 2 = outstanding principal 100 + remaining interest 15 = Rs. 115
Verification / Alternative check:
Another viewpoint is to compute interest separately on the first year and second year outstanding amounts and ensure the total of all payments equals principal plus total interest. Here total interest is Rs. 15 and total payments are 100 at year 1 and 115 at year 2, giving 215. This equals principal 200 plus interest 15, so the amounts balance correctly.

Why Other Options Are Wrong:
Rs. 100 or Rs. 105 would not be enough to cover both the remaining principal and the interest for the second year. Rs. 110 also falls short of the total of principal and interest still due. Only Rs. 115 satisfies the condition that the borrower fully clears the loan and all interest by the end of 2 years.

Common Pitfalls:
Some students either ignore the interim payment or incorrectly assume that interest is charged on the full original principal for the full 2 years, which would be more appropriate for a different interpretation. It is important to reason clearly about how interest is charged on the outstanding amount year by year in this type of exam question.

Final Answer:
The borrower must pay Rs. 115 at the end of 2 years to clear all dues.