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 4/13 of H’s pres…

Let the present ages of R and S be 3x and 2x respectively since their present age are in the ratio 3 : 2.

R's present age is 4/13 of H's present age

i.e. 3x = 4/13 × 117

3x = 4 × 9

3x = 36

x = 12

Thus, the present age of R is 3 × 12 = 36 years.

The present age of S is 2 × 12 = 24 years.

Let the no. of years after which the ratio of the ages of R and S would be 15 : 11 be z.

Age of R/Age of S = 15/11

36 + z/24 + z = 15/11

(36 + z) × 11 = 15 × (24 + z)

396 + 11z = 360 + 15z

4z = 396 - 360

4z = 36

z = 9

Hence, after 9 years, the ages of R and S would be in the ratio of 15 : 11.