Solve this multiple-choice question and choose the correct option.

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).

Curioustab

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.

Verbal Reasoning Data Sufficiency Difficulty: Easy

Choose an option

A

Only I
B

Only II
C

Either I or II (III is not needed)
D

I and III
E

None of these

Answer

Correct Answer: Either I or II (III is not needed)

Explanation

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.