BD on a certain sum for 3 years is Rs 1116; the true discount on the same sum for 4 years is Rs 1200. Find the simple interest rate (percent per annum).

Introduction / Context:
Two time horizons with BD and TD on the same face value pin down the rate uniquely under simple interest. We eliminate the (unknown) face value to solve for r.

Given Data / Assumptions:

• BD (3 years) = Rs 1116.
• TD (4 years) = Rs 1200.
• Let face value be A and rate r% p.a.

Concept / Approach:
BD = A·r·t/100. For 3 years: BD₃ = A·r·3/100 = 1116 ⇒ A r = 37200. For 4 years, with k′ = 4r/100 = r/25, TD₄ = A·k′/(1 + k′) = 1200. Substitute A from the first relation and solve for r.

Step-by-Step Solution:

Verification / Alternative check:
Check: k′ = 0.24; TD₄ = A · 0.24/1.24. Since A r = 37200 → A = 37200/6 = 6200; TD₄ = 6200 · 0.24/1.24 = 1200.

Why Other Options Are Wrong:
Any other r fails the pair (1116, 1200) simultaneously.

Common Pitfalls:
Mistaking TD for A·r·t/100; that is BD, not TD.

Final Answer:
6%