The true discount on Rs. 1,760 at 12% simple interest is Rs. 160. After how much time is it due?

Given data

• A = Rs. 1,760
• TD = Rs. 160
• Rate r = 12% p.a.

Concept

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

Steps
160 = 1760 × x / (1 + x)160 + 160x = 1760x ⇒ 160 = 1600x ⇒ x = 0.1r t = 0.1 ⇒ t = 0.1 / 0.12 = 0.833… year = 10 months

Final Answer
Time due = 10 months.