Banker’s Discount (BD) and Banker’s Gain (BG) on a certain bill are ₹196 and ₹28, respectively. Using standard BD–TD–BG relations for simple interest bills, determine the face value (amount due at maturity) of the bill.

Introduction / Context:This question uses the classic relationships among Banker’s Discount (BD), True Discount (TD), Banker’s Gain (BG), and the face value F of a bill under simple interest conventions. We will extract TD and then back-compute F.

Given Data / Assumptions:

• BD = ₹196.
• BG = ₹28.
• All discounts follow simple interest bill-discounting definitions.

Concept / Approach:Key identities (with x = r * t): BD = F * x, TD = F * x / (1 + x), BG = BD − TD. Also BD/TD = 1 + x and BG = x * TD. If BD and BG are known, TD = BD − BG immediately. Then 1 + x = BD/TD ⇒ x obtained; next F = BD / x.

Step-by-Step Solution:

Verification / Alternative check:Compute TD from F and x: TD = F*x/(1+x) = 1176*(1/6)/(7/6) = 1176*(1/7) = ₹168; BG = 196 − 168 = ₹28, consistent.

Why Other Options Are Wrong:₹1200, ₹1376, and ₹1400 do not satisfy BD/TD = 7/6 while keeping BD = ₹196.

Common Pitfalls:Confusing BD with TD or forgetting that BG = BD − TD; mixing rate and time unnecessarily when x can be inferred from BD/TD.

Final Answer:₹ 1176