Find the face value from interest and discount on the same sum: The simple interest on a certain sum is ₹67.20 and the (true) discount on the same sum for the same time and rate is ₹60. Find the sum (face value).

Introduction / Context:
There is a classic relation between simple interest (I) on a sum and the true discount (D) on the same sum for the same time and rate: the face value A equals (I * D) / (I − D). This follows from writing I and D in terms of A and r t and eliminating r t.

Given Data / Assumptions:
I = ₹67.20, D = ₹60, same time and rate for both measures on the same sum.

Concept / Approach:
Derivation outline: If I = A * x and D = A * x / (1 + x) with x = r t, then I − D = A * x^2 / (1 + x). Thus (I * D)/(I − D) = A.

Step-by-Step Solution:

Verification / Alternative check:
Compute x from either I/A or D/(A − D): I/A = 67.20/560 = 0.12; D/(A − D) = 60/500 = 0.12. Consistent.

Why Other Options Are Wrong:
They do not satisfy the identity A = (I * D)/(I − D) for the given I and D.

Common Pitfalls:
Interpreting “discount” as banker’s discount; here “discount” is the true discount unless stated otherwise in this relation.

Final Answer:
Rs. 560