Simple Interest – Time for a larger multiple at the same rate: A sum becomes twofold (double) in 6 years at a certain simple interest rate. At the same annual rate, in how many years will the same sum become tenfold?

Introduction / Context:
With simple interest, the amount grows linearly in time: A = P * (1 + r * t). Knowing the time to double fixes the rate; we can then scale to any target multiple.

Given Data / Assumptions:

• Twofold in 6 years → 1 + r * 6 = 2
• Same r to reach tenfold → 1 + r * T = 10

Concept / Approach:
Compute r from the doubling condition and plug that r into the tenfold condition to obtain T.

Step-by-Step Solution:
1 + 6r = 2 → 6r = 1 → r = 1/6 per year = 16 2/3 %1 + (1/6) * T = 10 → T/6 = 9 → T = 54 years

Verification / Alternative check:
At r = 1/6, the linear term after 54 years is r * T = 9; 1 + 9 = 10 → tenfold (correct).

Why Other Options Are Wrong:
35, 49, and 59 years do not satisfy 1 + r * T = 10 when r = 1/6.

Common Pitfalls:
Using compound-interest reasoning or misreading 'twofold' as 200% interest (it is 100% over principal).

Final Answer:
54 yr