Banker’s Gain known (8 years @ 24%) → Present Worth: The banker's gain of a sum due 8 years hence at 24% per annum is ₹ 144. Find the present worth of that bill.

Introduction / Context:Given BG and the product x = r * t, we can compute F using BG = F * x^2 / (1 + x), then present worth P = F / (1 + x). Here r is large and t is long, so x > 1, but the simple-interest relationships still apply.

Given Data / Assumptions:

• r = 24% per annum; t = 8 years ⇒ x = r * t = 0.24 * 8 = 1.92.
• BG = ₹ 144.

Concept / Approach:Compute F from the BG identity, then divide by (1 + x) to get P.

Step-by-Step Solution:BG = F * x^2 / (1 + x) ⇒ F = BG * (1 + x) / x^2 = 144 * 2.92 / (1.92^2).1.92^2 = 3.6864; hence F ≈ 144 * 2.92 / 3.6864 ≈ 144 * 0.7920 ≈ ₹ 114.05.P = F / (1 + x) = 114.05 / 2.92 ≈ ₹ 39.06.

Verification / Alternative check:BD = F * x ≈ 114.05 * 1.92 ≈ 219.0; TD = F * x / (1 + x) ≈ 219.0 / 2.92 ≈ 75.0; BG = BD − TD ≈ 144, matching the given.

Why Other Options Are Wrong:45, 38.06, 50, 36 are off once the precise BG relation is applied.

Common Pitfalls:Using compound-interest discounting; rounding too early; miscomputing x = r * t.

Final Answer:₹ 39.06