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

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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) About Me  (Show Source):
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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

%28x%2By%29%2F%28x-y%29=2%2F1
2x-2y=x%2By
x=3y [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

%28x%2By-8%29%2F%28x-y%29=3%2F2
2x%2B2y-16=3x-3y
5y-16=x [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.

3y=5y-16
2y=16
y=8 [3]

Use [1] and [3] to find x.
x=3%288%29=24

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