The banker’s gain (BG) on a bill due 2 years hence at 5% p.a. is ₹8. Find the present worth (PW) of the bill.

Introduction / Context:
Given banker’s gain and (rate × time), there is a direct formula linking BG and PW (present worth): BG = x^2 * PW with x = r * t. This avoids computing face value first.

Given Data / Assumptions:

• r = 5% p.a., t = 2 years.
• BG = ₹8.

Concept / Approach:
Let x = r * t = 0.05 * 2 = 0.10. Identities: PW = F / (1 + x); TD = x * PW; BG = x * TD = x^2 * PW. Hence PW = BG / x^2.

Step-by-Step Solution:

Verification / Alternative check:
If PW = 800 and x = 0.1, then TD = x * PW = 80; BG = x * TD = 0.1 * 80 = 8, as given.

Why Other Options Are Wrong:
₹650, ₹750, and ₹850 do not satisfy BG = x^2 * PW with x = 0.1.

Common Pitfalls:
Trying to compute face value F or rate separately; the compact identity BG = x^2 * PW is sufficient.

Final Answer:
Rs. 800