Banker’s Discount equals True Discount: The banker's discount on ₹1600 at 6% per annum is the same as the true discount on ₹1624 for the same time and rate. Determine the time period (express your answer in months).

Introduction / Context:
In banking arithmetic, three linked quantities appear for a bill due after time t at simple interest rate r: Banker's Discount (BD), True Discount (TD), and Banker's Gain (BG). For face value A, BD is the simple interest on A for the remaining time; TD is the reduction needed so that the present worth grows to A in time t at rate r. Here, BD on ₹1600 equals TD on ₹1624 at the same r and t. We must find t in months.

Given Data / Assumptions:

• Face values: A1 = ₹1600, A2 = ₹1624
• Rate r = 6% per annum (0.06)
• Time = t years (unknown)
• Equality: BD(A1) = TD(A2)

Concept / Approach:
Formulas (simple interest):

Step-by-Step Solution:

Verification / Alternative check:
If t = 3 months, r t = 0.06 * 0.25 = 0.015. Then BD(1600) = 1600 * 0.015 = ₹24, TD(1624) = 1624 * 0.015 / 1.015 ≈ ₹24.00. Values match.

Why Other Options Are Wrong:
4, 6, or 8 months yield r t values that make BD and TD unequal for the given amounts.

Common Pitfalls:
Confusing TD with BD or using TD = A * r * t (incorrect). TD must divide by (1 + r t). Also ensure t is in years before converting to months.

Final Answer:
3 months