At what rate percent per year will a sum double itself in $6\dfrac{1}{4}$ years?

Given:

T = $6\dfrac{1}{4}$ years

= $\dfrac{25}{4}$ years

A = 2P

$\text{A = P + S.I.}\\[1em] \Rightarrow \text{2P = P + S.I.}\\[1em] \Rightarrow \text{2P - P = S.I.}\\[1em] \Rightarrow \text{P = S.I.}\\[1em]$

Let rate of interest be $r$.

$\because \text{S.I.} = ₹ \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \text{P} = ₹ \Big(\dfrac{P \times r \times 25}{4 \times 100}\Big)\\[1em] \Rightarrow \cancel {P} = ₹ \dfrac{\cancel {P} \times r \times 25}{400}\\[1em] \Rightarrow 1 = ₹ \dfrac{25r}{400}\\[1em] \Rightarrow \text{400} = 25r\\[1em] \Rightarrow r = \dfrac{400}{25}\\[1em] \Rightarrow r = 16$

Hence, the rate of interest = 16%.