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.