Simple Interest — A sum becomes three times in 20 years at simple interest. In how many years will it become double at the same rate?

Introduction / Context:
First use the tripling information to deduce the rate under simple interest, then reuse that rate to find the doubling time.

Given Data / Assumptions:

• A = 3P in 20 years (simple interest).
• Same rate is used to find time to double.

Concept / Approach:
If A = 3P, then SI = 2P over 20 years. Hence P * r * 20 = 2P ⇒ r = 2/20 = 0.10 = 10% p.a.

Step-by-Step Solution:
Rate r = 10% per annum.To double: need SI = P.P = P * r * t ⇒ P = P * 0.10 * t ⇒ t = 10 years.

Verification / Alternative check:
At 10% for 10 years: SI = P; amount = 2P.

Why Other Options Are Wrong:
8, 12, 14, 16 years do not match r = 10% derived from the tripling data.

Common Pitfalls:
Carrying compound interest ideas into a simple interest setting.

Final Answer:
10 yr