In what time will the interest on a certain sum of money at 6% be $\dfrac{5}{8}$ of itself?

Let the Principal amount be ₹ P.

S.I. = $\dfrac{5}{8}$ of P

R = 6%

Let time be $t$ years.

$\because \text{S.I.} = ₹ \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \dfrac{5}{8} \times \text{P} = ₹ \Big(\dfrac{P \times 6 \times t}{100}\Big)\\[1em] \Rightarrow \dfrac{5}{8} \times \cancel{P} = ₹ \Big(\dfrac{\cancel{P} \times 3t}{50}\Big)\\[1em] \Rightarrow \dfrac{5}{8} = ₹ \Big(\dfrac{3t}{50}\Big)\\[1em] \Rightarrow t = \dfrac{5 \times 50}{8 \times 3}\\[1em] \Rightarrow t = \dfrac{250}{24}\\[1em] \Rightarrow t = 10\dfrac{10}{24}\\[1em] \Rightarrow t = 10\dfrac{5}{12}\\[1em]$

Hence, the time is 10 years and 5 months.