On ₹ 371, the true discount for a certain time is ₹ 21. For double that time at the same rate, what will be the true discount on the same amount?

Introduction / Context:
True Discount (TD) varies nonlinearly with time because TD = F * x/(1 + x) where x = r * t. Doubling time doubles x but not TD linearly; hence we evaluate TD at 2x.

Given Data / Assumptions:

• F = 371
• TD at time t = 21
• Need TD at 2t, same rate r

Concept / Approach:
From TD = F * x/(1 + x), obtain x at time t, then compute TD at 2x.

Step-by-Step Solution:
21 = 371 * x/(1 + x) → 21(1 + x) = 371x. 21 = (371 − 21)x → x = 21/350 = 0.06. At double time, x' = 2x = 0.12. TD(2t) = 371 * 0.12/(1 + 0.12) = 371 * 0.12/1.12 = 39.75.

Verification / Alternative check:
Compute present worths: P(t) = 371/(1 + 0.06) = 350; P(2t) = 371/(1 + 0.12) = 331.25; TD(2t) = 371 − 331.25 = 39.75.

Why Other Options Are Wrong:
39.00 and 38.85 underestimate the nonlinear increase; 40.00 overshoots; 35.75 is far from the exact computed value.

Common Pitfalls:
Assuming TD doubles when time doubles; forgetting the denominator (1 + x) that moderates growth.

Final Answer:
₹ 39.75