Ratio Proportion on Ages

A favorite question that appears more often than not from the Ratio Proportion topic is that of comparing the ages of two people.

Here is an example of such a question.

Question

The ratio of the present ages of Shreyas and Swetha is 3 : 5. Six years back Swetha was twice as old as Shreyas was. How old is Shreyas now?

1. 24
2. 12
3. 30
4. 18
5. 36

Correct Answer is choice (4). 18 years

Explanatory Answer

Let the present age of Shreyas be x years and that of Swetha be y years.
Therefore, x : y :: 3 : 5

Or x/y = 3/5
or x = (3/5)y. --- eqn (1)

6 years back Shreyas was (x - 6) years old.
6 years back Swetha was (y - 6) years old.

We know that Swetha was twice as old as Shreyas was 6 years back.
So, (y - 6) = 2(x - 6) --- eqn (2).

Substituting x = (3/5)y from eqn (1) in eqn (2) we get
(y - 6) = 2((3/5)y - 6)
or 5(y - 6) = 2(3y - 30)
or 5y - 30 = 6y - 60
or y = 30.

x = (3/5)y = (3/5)*30 = 18 years.

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