In banker's discount, the banker's discount on a certain sum of money is Rs. 72 and the true discount on the same sum for the same period of time is Rs. 60. What is the sum due (the amount payable at maturity)?

Introduction / Context:
Questions on banker's discount and true discount are common in commercial arithmetic. They test your understanding of present worth, sum due (amount), and how banks calculate interest on bills that are payable at a future date. Here, you are given both the banker's discount and the true discount and are asked to find the sum due at maturity.

Given Data / Assumptions:

The banker's discount (BD) on a bill = Rs. 72.
The true discount (TD) on the same bill for the same time = Rs. 60.
We are asked to find the sum due, i.e., the amount payable at maturity (A).
The rate of interest and time are the same for BD and TD, but their exact values are not required for this problem.

Concept / Approach:
True discount is the difference between the amount due at maturity and its present worth. Banker's discount is simple interest calculated on the amount due (face value) for the unexpired time. An important relationship between BD, TD and the amount A is:
A = (BD * TD) / (BD - TD) This formula is derived from the basic simple interest formulas and the definition of banker's gain, but we can apply it directly here since BD and TD are known.

Step-by-Step Solution:
Step 1: Note BD and TD. BD = Rs. 72, TD = Rs. 60. Step 2: Use the formula for the amount (sum due). A = (BD * TD) / (BD - TD). Step 3: Substitute the values. A = (72 * 60) / (72 - 60). A = 4320 / 12. A = Rs. 360.

Verification / Alternative check:
We know banker's gain (BG) = BD - TD = 72 - 60 = Rs. 12. Another identity is BG * A = BD * TD. So 12 * A = 72 * 60 = 4320, hence A = 4320 / 12 = 360, which matches the result above. This cross-check confirms the correctness of the calculation.

Why Other Options Are Wrong:
Rs. 290 and Rs. 420 do not satisfy the relationship A = (BD * TD) / (BD - TD); if substituted, they would not preserve the necessary ratio between BD and TD.
Rs. 480 is larger than the product-based value and contradicts the equations derived from simple interest relationships between BD and TD.

Common Pitfalls:
Students often confuse true discount with banker's discount and attempt to treat both as the same quantity. Others try to use simple interest directly without recalling the specific derived formula linking BD, TD, and amount. Remember that when both BD and TD are given, using A = (BD * TD) / (BD - TD) is the fastest and safest approach.

Final Answer:
The sum due at maturity is Rs. 360.