Simple Interest – Split lending at two rates: Subbarao has ₹ 2,540. He lends part at 12% per annum and the rest at 12.5% per annum. After one year, the total interest received is ₹ 311.60. How much did he lend at 12% per annum?

Introduction / Context:This is a direct linear equation application of simple interest with two parts of the same principal lent at different rates.

Given Data / Assumptions:

• Total principal = ₹ 2540
• Part 1 at 12%; Part 2 at 12.5%
• Total interest in 1 year = ₹ 311.60

Concept / Approach:Let x be the amount at 12%. Then (2540 - x) is at 12.5%. Total interest (1 year) = 0.12x + 0.125(2540 - x).

Step-by-Step Solution:0.12x + 0.125(2540 - x) = 311.600.12x + 317.50 - 0.125x = 311.60-0.005x = -5.90 → x = 1180

Verification / Alternative check:Interest = 0.12*1180 + 0.125*1360 = 141.60 + 170.00 = 311.60 (matches).

Why Other Options Are Wrong:₹ 1360, ₹ 1340, and ₹ 1240 produce totals different from ₹ 311.60 when substituted.

Common Pitfalls:Mixing rupee and percentage arithmetic or misplacing x between the two rates.

Final Answer:₹ 1180