Aptitude Hack#65(29-4-19)

Question:

If 13:11 is the ratio of the present age of Jothi and Viji respectively and 15:9 is the ratio between Jothi's age 4 years hence and Viji's age 4 years ago. Then what will be the ratio of Jothi's age 4 years ago and Viji's age 4 years hence?

 A)  15: 9

 B)  9: 5

 C)  11 : 13

 D) 12:15

 E)  16: 5


 Answer: C) 11: 13

Explanation:

Let the present age of Jothi and Viji be 13X and 11X respectively.

Given, Jothi's age 4 years hence and Viji's age 4 years ago in the ratio 15:9.
That is, (13X + 4) / (11X - 4) = 15 / 9
=> 9 (13X + 4) = 15 (11X - 4)
=> 117X + 36 = 165X - 60
=> 165X - 117X = 60 + 36
=> 48X = 96
=> X = 96 / 48
=> X = 2

Now, Required ratio = (13X - 4) / (11X + 4)
on substituting value of X = 2 we get,
= [13(2)-4] / [11(2)+4]
= 22/26
= 11/13

Hence the answer is 11:13