What is the annual rate of interest (per annum)? I. An amount doubles at simple interest in 10 years. II. The difference between compound interest and simple interest on ₹ 15,000 for 2 years is ₹ 150. III. Compound interest after 8 years exceeds the principal.

Introduction / Context:
We must identify which statements suffice to find the unique annual rate r.

Reasoning:

• I alone: At simple interest A = P(1 + r t). Doubling in 10 years ⇒ 2P = P(1 + 10r) ⇒ r = 0.1 = 10% p.a. Sufficient.
• II alone: For 2 years, CI − SI = P*(r/100)^2. So 150 = 15000*(r^2)/10000 ⇒ r^2 = 100 ⇒ r = 10% (taking positive rate). Sufficient.
• III: “CI after 8 years exceeds principal” only implies r > 0, which does not fix r. Insufficient.

Why Other Options Are Wrong:
Neither “Only I” nor “Only II” captures that both I or II, individually, suffice; combining I with III is unnecessary.

Final Answer:
Either I or II is sufficient (III is irrelevant).