Simple interest on a certain sum is $\dfrac{16}{25}$ of the sum. Find the rate of interest and time, if both are numerically equal.

Given:

S.I. = $\dfrac{16}{25}$ of P

Rate of interest = Time = $x$

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \dfrac{16}{25}P = \Big(\dfrac{P \times x \times x}{100}\Big)\\[1em] \Rightarrow \dfrac{16}{25}\cancel{P} = \Big(\dfrac{\cancel{P} \times x \times x}{100}\Big)\\[1em] \Rightarrow x^2 = \dfrac{16\times100}{25}\\[1em] \Rightarrow x^2 = 64\\[1em] \Rightarrow x = \sqrt{64}\\[1em] \Rightarrow x = 8\\[1em]$

Hence, rate = 8% and time = 8 years.