# The ratio of ages of R and S, 3 years ago was 5 : 7 and the ratio of age of T and U, 3 years from now will be 11 : 5. At present, T is 6 years older t

19 views

closed

The ratio of ages of R and S, 3 years ago was 5 : 7 and the ratio of age of T and U, 3 years from now will be 11 : 5. At present, T is 6 years older than S. The average age of R and U is 15 years.

From the statement given in the above question, which of the following can be determined?

(A) Present age of R (B) Present age of S (C) Present age of T (D) Present age of U
1. Only S and T
2. Only R and U
3. Only R, S and U
4. All R, S, T, U
5. None of them

by (110k points)
selected

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.