If a sum of money becomes \(\frac{11}{8}\) times in 7.5 years at simple rate of interest, then at the same rate of interest it will becomes \(\frac{19}{12}\) times in:

11 years 8 months

Let principal be P and  rate be R,

Amount = P(1 + \(\frac{7.5R}{100}\))

⇒ \(\frac{11}{8}\)P = P(1 + \(\frac{7.5R}{100}\))

⇒ \(\frac{11}{8}\) = 1 + \(\frac{7.5R}{100}\)

⇒ \(\frac{7.5R}{100}\) = \(\frac{3}{8}\)

⇒ R = 5

Now, 

⇒ \(\frac{19}{12}\) = P(1 + \(\frac{5T}{100}\))

⇒ \(\frac{19}{12}\) = 1 + \(\frac{5T}{100}\)

⇒ T = \(\frac{35}{3}\)

      = 11 years 8 months