On simple interest a certain sum becomes 160% of itself in 5 years at a certain rate of interest per annum. In how many years will the sum double itself under the same rate of interest?

Correct option is C

Given:

A = 160% of Principal = 1.6P
Time (T) = 5 years
Simple Interest (SI) = A - P = 1.6P - P = 0.6P
Formula Used:

Simple Interest (SI) = $$\frac{(P × R × T) }{ 100}$$​​
To double the sum: A = 2P → SI = 2P - P = P
Solution:

Use SI formula to find Rate (R):

​$$\begin{aligned}0.6P &= \frac{P \times R \times 5}{100} \\ \ \\0.6 &= \frac{R \times 5}{100} \quad \\\ \\R &= \frac{0.6 \times 100}{5} = 12\%\end{aligned}$$​​
Use the same formula to find time to double the sum:
​$$\begin{aligned}& P = \frac{P \times 12 \times T}{100} \\\ \\\Rightarrow \quad & 1 = \frac{12 \times T}{100} P \text{)} \\\ \\\Rightarrow \quad & T = \frac{100}{12} = 8.33\ \text{years} = 8 \tfrac{1}{3}\ \text{years}\end{aligned}$$​​
The sum will double itself in $$8\frac{ 1}{ 3}$$​years.