If ₹ 10 is the true discount on a bill of ₹ 110 due at the end of a certain time, then what discount would be allowed on the same amount due at the end of double the time (same rate, simple interest)?

Introduction / Context:
True discount increases nonlinearly with time. Given TD at time t, we find TD at 2t using the TD formula.

Given Data / Assumptions:

• F = 110
• TD(t) = 10
• Need TD(2t) at same rate

Concept / Approach:
TD = F * x/(1 + x) where x = r * t. First get x from TD(t), then compute TD at 2x.

Step-by-Step Solution:
10 = 110 * x/(1 + x) → x = 10/(110 − 10) = 10/100 = 0.1. At double time, x' = 0.2. TD(2t) = 110 * 0.2/(1.2) = 110 * (1/6) = 18.333... ≈ ₹ 18.33.

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

Why Other Options Are Wrong:
₹ 20 and ₹ 22 assume linear doubling; ₹ 21.81 is not the exact rational outcome; ₹ 19.80 does not follow from the formula.

Common Pitfalls:
Assuming TD doubles with time; ignoring the (1 + x) denominator.

Final Answer:
₹ 18.33