Question

At what rate percent per annum simple interest will a sum double itself in 10 years?

(a) 8%
(b) 10%
(c) 12%
(d) $12\frac{1}{2}$%

Answer 1

Amount = 2 times the sum = 2P

Simple interest (I) = Amount − Sum = 2P − P = P

Let the sum (P) be x.
Then, simple interest (I) = x
Rate (R) = R%
Time (T) = 10 years

$$\begin{gathered} I=\frac{P\times R\times T}{100} \\ \Rightarrow R=\frac{100\times I}{P\times T} \\ =\frac{100\times x}{x\times {\displaystyle 10}} \\ =10\% \end{gathered}$$

Hence, the correct option is (b).