Rs. 20 is the true discount on Rs. 260 due after time t. What is the true discount on the same sum due after t/2 (rate unchanged)?

Given data

• A = Rs. 260
• TD at time t is Rs. 20
• Find TD at time t/2 (same r)

Concept

TD = A × (r t) / (1 + r t). Let x = r t.

Steps
20 = 260 × x / (1 + x) ⇒ 20 + 20x = 260x ⇒ 20 = 240x ⇒ x = 1/12At t/2: x/2 = 1/24TD = 260 × (1/24) / (1 + 1/24) = 260 × (1/24) × (24/25) = 260/25 = 10.40

Final Answer
True discount = Rs. 10.40.