A certain sum was invested on simple interest. The amount to which it had grown in 5 years was 1\(\frac{1 }{4}\) times the amount to which it had grown in 3 years. The percentage rate of interest was:

20%

Amount in 5 years = P + \(\frac{P\;×\;R\;×\;5}{100}\) ---(i)

Amount in 3 years = P + \(\frac{P\;×\;R\;×\;3}{100}\) ---(ii)

According to the question,

⇒ (P + \(\frac{P\;×\;R\;×\;5}{100}\)) = \(\frac{5}{4}\) x (P + \(\frac{P\;×\;R\;×\;3}{100}\))

⇒ (1 + \(\frac{5R}{100}\)) = \(\frac{5}{4}\) x ( + \(\frac{3R}{100}\))

⇒ (5 - \(\frac{15}{4}\)) x \(\frac{R}{100}\) = \(\frac{1}{4}\)

⇒ \(\frac{5R}{100\;×\;4}\) = \(\frac{1}{4}\)

⇒ R = 20%