If ₹ 10 is allowed as true discount on a bill of ₹ 110 due at the end of a certain time, then what discount would be allowed on the same sum due at the end of double the time?

Introduction / Context:
We reuse the true discount formula to find TD at double the time given TD at the initial time.

Given Data / Assumptions:

• F = 110
• TD(t) = 10
• Find TD(2t)

Concept / Approach:
If TD = F * x/(1 + x) at time t, where x = r*t, then at 2t the parameter is 2x and TD(2t) = F * 2x/(1 + 2x).

Step-by-Step Solution:
x = 10/(110 − 10) = 0.1. TD(2t) = 110 * 0.2/1.2 = 110/6 = 18.333... → Rs. 18.33.

Verification / Alternative check:
Present worths: P(t) = 110/1.1 = 100; P(2t) = 110/1.2 ≈ 91.666...; TD(2t) ≈ 18.333....

Why Other Options Are Wrong:
20 and 22 assume linearity; 21.81 and 19.00 are not consistent with the precise ratio.

Common Pitfalls:
Assuming TD doubles with time; forgetting to recompute using 2x.

Final Answer:
Rs. 18.33