Present age of R and S are in the ratio of 3 : 2 respectively. If the present age of H is 117 years and R’s present age is $$\frac{4}{13}$$ of H’s present age, then after how many years the ages of R and S would be in the ratio of 15 : 11?

Present age of H = $$117$$ years

=> R’s present age = $$\frac{4}{13}\times117=36$$ years

Thus, S's present age = $$\frac{2}{3}\times36=24$$ years

Let after $$x$$ years, the ages of R and S would be in the ratio = $$15:11$$

=> $$\frac{36+x}{24+x}=\frac{15}{11}$$

=> $$396+11x=360+15x$$

=> $$15x-11x=396-360$$

=> $$x=\frac{36}{4}=9$$

$$\therefore$$ After 9 years, the ages of R and S would be in the ratio of 15 : 11

=> Ans - (A)