Simple Interest – Income drop when rate falls from 13% to 12.5%: A moneylender’s yearly income decreases by ₹ 104 when his rate falls from 13% to 12.5% per annum. Find his capital.

Introduction / Context:
Annual simple-interest income is proportional to both the rate and the capital. A small percentage drop producing a known rupee decrease allows direct computation of capital via proportional reasoning.

Given Data / Assumptions:

• Old rate r1 = 13% per annum
• New rate r2 = 12.5% per annum
• Annual income drop ΔI = ₹ 104
• Capital C is constant

Concept / Approach:
Income each year equals C * r / 100. Thus ΔI = C * (r1 − r2) / 100. Solve C = (ΔI * 100) / (r1 − r2).

Step-by-Step Solution:
Rate difference = 13% − 12.5% = 0.5% = 0.5C = (104 * 100) / 0.5 = 10,400 / 0.5 = 20,800

Verification / Alternative check:
At 13%, income = 0.13C; at 12.5%, income = 0.125C; difference = 0.005C. With C = 20,800, 0.005C = 104, as given.

Why Other Options Are Wrong:
Other capitals produce income differences not equal to ₹ 104 under a 0.5% change, hence they violate the given condition.

Common Pitfalls:
Interpreting 0.5% as 0.5 (without dividing by 100) or mixing per-annum values with multi-year totals leads to errors. Here, the change is explicitly per year.

Final Answer:
₹ 20,800