SOLUTION: The ratio of sum and the difference of the present age of Vivek and Arvind are 2: 1. Four years ago, this ratio was 3:2. What will be the ratio of their ages after 12 years

Question 1199556: The ratio of sum and the difference of the present age of Vivek and Arvind are 2: 1. Four years ago, this ratio was 3:2. What will be the ratio of their ages after 12 years
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

let x = Vivek's current age
let y = Arvind's current age

The sum of their ages is x+y; the difference of their ages is x-y.

The ratio of the sum of their ages and the difference of their ages is 2:1

[1]

Vivek's age 4 years ago was x-4; Arvind's age 4 years ago was y-4.
The sum of their ages 4 years ago was x+y-8; the difference of their ages 4 years ago was (still!) x-y.
Four years ago, the ratio of the sum of their ages and the difference of their ages was 3:2

[2]

[1] and [2] show two different expressions in terms of y for variable x. Set those two expressions equal to each other and solve for y.

[3]

Use [1] and [3] to find x.

Their current ages are Vivek = x = 24 and Arvind = y = 8.

Their ages 12 years from now will be Vivek = 24+12 = 36 and Arvind = 8+12 = 20.

The ratio of their ages 12 years from now will be 36:20 = 9:5

ANSWER: 9:5

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