A person takes a loan of ₹ 200 at 5% simple interest. He returns ₹ 100 at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay :

### Concept & Logic When partial payments are made against a loan, the interest is calculated on the outstanding balance for the respective time period. ### Step-by-Step Solution * **Given:** Principal = ₹ 200, Rate = 5% p.a., Time = 1 year (initial period). * **Calculation:** Interest for the 1st year = $\frac{200 \times 5 \times 1}{100}$ = ₹ 10. * Total amount owed at the end of 1st year = ₹ 200 + ₹ 10 = ₹ 210. * He returns ₹ 100. So, the new outstanding principal for the 2nd year = $210 - 100$ = ₹ 110. * Interest for the 2nd year = $\frac{110 \times 5 \times 1}{100}$ = ₹ 5.50. * Total amount to clear the dues at the end of 2nd year = Outstanding Principal + Interest = ₹ 110 + ₹ 5.50 = ₹ 115.50. ### Exam Strategy & Shortcut Calculate sequentially: Add 5% of 200 (10), subtract 100, then add 5% of the remaining 110 (5.5). $200 + 10 - 100 = 110$. $110 + 5.5 = 115.5$. ### Common Pitfall Many students subtract the ₹ 100 payment directly from the original principal (₹ 200) without accounting for the first year's interest, leading to an incorrect outstanding principal of ₹ 100 and an incorrect final payment of ₹ 105. ### Final Answer Therefore, the correct answer is **₹ 115.50**.