Rate cut and withdrawal — back-solve original deposit: When a bank reduces its annual simple interest rate from 6.5% to 5.5%, a depositor withdraws ₹ 600. As a result, the depositor’s annual interest falls by ₹ 73. What was the original deposit amount before the withdrawal?

Introduction / Context:
A simultaneous change in rate and principal requires writing the before/after annual interest and taking their difference. Because we are in simple interest, the annual interest is directly P * r / 100.

Given Data / Assumptions:

• Original principal = D (unknown)
• Original rate r1 = 6.5% p.a.
• New rate r2 = 5.5% p.a.
• Withdrawal W = ₹ 600 → new principal = D − 600
• Drop in annual interest = ₹ 73

Concept / Approach:
Write I1 − I2 = 73 with I1 = 0.065D and I2 = 0.055(D − 600). Solve for D.

Step-by-Step Solution:
0.065D − 0.055(D − 600) = 730.065D − 0.055D + 0.055 * 600 = 730.01D + 33 = 73 → 0.01D = 40 → D = ₹ 4000

Verification / Alternative check:
Before: 6.5% of 4000 = ₹ 260. After: 5.5% of (4000 − 600) = 5.5% of 3400 = ₹ 187. Difference = 260 − 187 = ₹ 73 (checks).

Why Other Options Are Wrong:
Substituting ₹ 6000, ₹ 7000, or ₹ 9000 does not yield exactly a ₹ 73 drop in annual interest.

Common Pitfalls:
Sign mistakes when expanding −0.055(D − 600) and unit slips when moving between percent and decimal form.

Final Answer:
₹ 4000