From PW = Rs 1100 and TD = Rs 110: find BD and banker’s gain: A bill has present worth Rs 1100 and true discount Rs 110. Compute the banker’s discount (BD) and the extra gain (banker’s gain, BG).

Introduction / Context:
As before, let x = r * t. Then PW = S / (1 + x), TD = S * x / (1 + x), BD = S * x, and BG = BD − TD = S * x^2 / (1 + x). With PW and TD given, all quantities follow directly.

Given Data / Assumptions:

• PW = 1100; TD = 110 → S = 1210.

Concept / Approach:
From PW = S / (1 + x) and TD = S * x / (1 + x) = PW * x, we get x = TD / PW = 110 / 1100 = 0.1. Hence BD = S * x and BG = BD − TD.

Step-by-Step Solution:

Verification / Alternative check:
TD = Sx/(1 + x) = 1210*0.1/1.1 = 110 ✔️; BG = Sx^2/(1 + x) = 1210*0.01/1.1 = 11 ✔️.

Why Other Options Are Wrong:
Other pairs do not satisfy both the TD identity and the BG definition simultaneously.

Common Pitfalls:
Confusing TD with BD; using S instead of PW to compute x.

Final Answer:
BD = Rs 121 and BG = Rs 11