Correct Answer - Option 4 : All R, S, T, U

Let the present age of R, S, T and U be ‘r’, ‘s’, ‘t’ and ‘u’ years respectively.

So, (r - 3)/(s – 3) = 5/7

⇒ 5s – 15 = 7r – 21

⇒ 7r – 5s = 6 ----(i)

Also, (t + 3) / (u + 3) = 11/5

⇒ 11u + 33 = 5t + 15

⇒ 5t – 11u = 18 ----(ii)

Now, t = s + 6

Putting in (ii)

5(s + 6) – 11 u = 18

⇒ 11u – 5s = 12

⇒ 11u + 6 – 7r = 12

⇒ 11u – 7r = 6 ----(iii)

Also, (r + u)/2 = 15

⇒ r + u = 30 ----(iv)

(iii) + 7 × (iv) given,

18u = 216

⇒ u = 12

∴ r = 30 – 12 = 18

From (i),

7 × 18 – 5s = 6

⇒ 5s = 120

⇒ s = 24

∴ t = s + 6 = 24 + 6 = 30

The present ages of all of them can be determined.