The ratio of the present ages of Oliver and Gulliver is same as the ratios of ages of Aram

and Oliver 9 years ago. 9 years from now, Gulliver will be as old as Aram was 9 years ago.

The present ages (in years) of exactly two of them are perfect squares, which is not true

for their ages 9 years hence. Which of the following can be the sum of the present ages

of Aram and Oliver?

A)59 B)49 C)69 D)79

Let the ages of Gulliver, Aram and Oliver be G, A and O respectively

G+9=A-9 =>A=G+18

O/G=(A-9)/(O-9)

O/G=(G+9)/(O-9)

O^2-9O=G^2+9G

O^2-G^2=9(O+G)

O-G=9 orO=9+G

If G=1 then, A=19 and O=10 hence, conditions are not satisfied.

If G=4, then A=22 and O=13 hence, conditions are not satisfied.

If G=9, then A=27 and O=18 hence, conditions are not satisfied.

If O=16, then G=7 and A=25 hence, conditions are not satisfied.

If O=25, then G=16 and A=34 for these values the conditions are satisfied.

Thus, the sum is 59.

I hope this helps!