The true discount on ₹ 936 at 8% per annum (simple interest) is ₹ 36. Find the time after which the amount is due.

Introduction / Context:
We determine the time of a bill given its true discount, face value, and annual rate. This uses the TD formula and solves for t.

Given Data / Assumptions:

• F = 936
• TD = 36
• r = 8% per annum

Concept / Approach:
TD = F * (r * t)/(1 + r * t). Solve for t via x = r * t.

Step-by-Step Solution:
36 = 936 * x/(1 + x). 36(1 + x) = 936x → 36 = 900x → x = 0.04. Since x = r * t = 0.08 * t, 0.08 * t = 0.04 → t = 0.5 years = 6 months.

Verification / Alternative check:
Present worth P = F/(1 + x) = 936/1.04 = 900. TD = F − P = 36, consistent.

Why Other Options Are Wrong:
3 or 9 months do not satisfy the equation; 1 year doubles x; 8 months similarly gives a mismatch.

Common Pitfalls:
Forgetting to convert years to months; mixing BD with TD; dropping the (1 + x) denominator.

Final Answer:
6 months