Question

Five years ago, A was three times as old as B and then 10 years later, a shall be twice as old as B. What are the present ages of A and B (in years)?
(A) 45, 15
(B) 30, 40
(C) 50, 30
(D) 50, 20

Answer 1

Hint: Assign variables to the present ages of A and B. then using the condition of 5 years ago, form one linear equation. And using the condition of 10 years later, form another linear equation. Then you will have two linear equations with two variables. Solve them to find the present ages of A and B.

Complete step-by-step answer:
Let the present age of A be $ x $
And the present age of B be $ y $
Then five years ago,
A’s age was $ x - 5 $
And B’s age was $ y - 5 $
 $ \Rightarrow (x - 5) = 3(y - 5) $
 $ \Rightarrow x - 5 = 3y - 15 $
 $ \Rightarrow x - 3y = - 10 $ . . . (1)
And after ten years
A’s age will be $ x + 10 $
And B’s age will be $ y + 10 $
 $ \Rightarrow (x + 10) = 2(y + 10) $
 $ \Rightarrow x + 10 = 2y + 20 $
 $ \Rightarrow x - 2y = 10 $ . . . (2)
By subtracting equation (2) from equation (1), we get
 $ - y = - 20 $
 $ \Rightarrow y = 20 $
By substituting this value in equation (2), we get
 $ x - 40 = 10 $
 $ \Rightarrow x = 50 $
Therefore, the present age of A and B is $50$ and $20$ respectively.
So, the correct answer is “Option D”.

Note: The key point in this question was to interpret the question properly. And since we assign variables to the present ages. You need to remember to add or subtract the number of years from those variables when you look into the future or past. Otherwise, the answer will be wrong. Once you form correct linear equations, then solving them is not difficult.