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.
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?
Correct Answer is choice (4). 18 years
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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