On a certain sum, the banker’s discount (BD) is ₹36 and the true discount (TD) is ₹30 for the same time and rate. What is the sum due (face value F)?

Introduction / Context:
Given BD and TD only, we can extract x = r * t using BD/TD, then use BD = F * x to compute the face value F directly. This avoids explicit rate/time values.

Given Data / Assumptions:

• BD = ₹36.
• TD = ₹30.

Concept / Approach:
Identity: BD/TD = 1 + x ⇒ x = BD/TD − 1 = 36/30 − 1 = 1/5. Then BD = F * x ⇒ F = BD / x.

Step-by-Step Solution:

Verification / Alternative check:
TD = F * x / (1 + x) = 180 * 0.2 / 1.2 = 36 / 1.2 = ₹30, matches.

Why Other Options Are Wrong:
₹120, ₹200, ₹220 do not satisfy both BD and TD under the same x.

Common Pitfalls:
Using TD = F * x (incorrect); TD is discounted by 1 + x in the denominator.

Final Answer:
Rs. 180