Split principal at 12% and 12.5% — find the 12% portion: A total of ₹ 2540 is lent in two parts, one at 12% p.a. and the other at 12.5% p.a. If the total annual interest is ₹ 311.60, how much is lent at 12%?

Introduction / Context:
When a principal is divided across two close rates, the total annual simple interest can be used to back-solve how much was placed at each rate by forming a single linear equation in one variable.

Given Data / Assumptions:

• Total principal = ₹ 2540
• Rate1 = 12% p.a.; Rate2 = 12.5% p.a.
• Total annual SI = ₹ 311.60
• Let x be the amount at 12%, so 2540 - x is at 12.5%

Concept / Approach:
Annual SI = sum of each part’s SI: 0.12x + 0.125(2540 - x) = 311.60. Solve for 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:
At 12%: 1180 * 0.12 = ₹ 141.60. At 12.5%: 1360 * 0.125 = ₹ 170. Total = ₹ 311.60 (checks out).

Why Other Options Are Wrong:
They do not satisfy the linear equation simultaneously with the known total ₹ 311.60.

Common Pitfalls:
Arithmetic slips on 12.5% (0.125) and sign errors when combining like terms can derail the solution.

Final Answer:
₹ 1180