The simple interest on a certain sum of money is $\dfrac{3}{8}$ of the sum in $6\dfrac{1}{4}$ years. Find the rate percent charged.

Given:

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

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

Let principal be P

S.I. = $\dfrac{3}{8}$ P

Let rate of interest be $r$.

$\because \text{S.I.} = ₹ \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \dfrac{3}{8}P = ₹ \Big(\dfrac{P \times r \times 25}{4 \times 100}\Big)\\[1em] \Rightarrow \dfrac{3P}{8} = ₹ \Big(\dfrac{P \times r \times 25}{400}\Big)\\[1em] \Rightarrow \dfrac{3}{8}\cancel {P} = ₹ \dfrac{\cancel {P} \times 25r}{400}\\[1em] \Rightarrow \dfrac{3}{8} = ₹ \dfrac{25r}{400}\\[1em] \Rightarrow r = \dfrac{3 \times 400}{8 \times 25}\\[1em] \Rightarrow r = \dfrac{1200}{200}\\[1em] \Rightarrow r = 6 \%$

Hence, the rate of interest = 6%.