Question

Ashwin’s age is four times his son’s present age. 4 years ago, Ashwin was 6 times as old as his son. Find the present’s age of Ashwin’s son.

Answer 1

Hint: Let us assume the present age of Ashwin as x and present age of son of Ashwin as y. In the question, it was given that Ashwin’s age is four times his son’s present age. From this statement, we can obtain the relation between x and y. Let us assume this equation as equation (1). In the question, it was given that 4 years ago, Ashwin was 6 times as old as his son. From this statement, we can obtain another relation between x and y. Let us assume this equation as equation (2). Now we will get the values of x and y by solving equation (1) and equation (2).

Complete step-by-step answer:
Let us assume the present age of Ashwin as x.
Let us assume the present age of son of Ashwin as y.
From the question, we are given that Ashwin’s age is four times his son’s present age.
So,
Age of Ashwin = (4) (Age of Ashwin’s son)
\[\Rightarrow x=4y..........(1)\]
From the question it is clear that 4 years ago, Ashwin was 6 times as old as his son.
Age of Ashwin before 4 years = x-4
Age of son of Ashwin before 4 years = y-4
So,
Age of Ashwin before 4 years = (6) (Age of Ashwin before 4 years)
\[\begin{align}
  & \Rightarrow x-4=6(y-4) \\
 & \Rightarrow x-4=6y-24 \\
 & \Rightarrow 6y=x+20.....(2) \\
\end{align}\]
Now we should substitute equation (1) in equation (2).
\[\begin{align}
  & \Rightarrow 6y=4y+20 \\
 & \Rightarrow 2y=20 \\
 & \Rightarrow y=10.....(3) \\
\end{align}\]
So, the present age of Ashwin’s son is equal to 10.
Now we should substitute equation (3) in equation (1).
\[\begin{align}
  & \Rightarrow x=4(10) \\
 & \Rightarrow x=40....(4) \\
\end{align}\]
So, the present age of Ashwin is equal to 40.
Hence, the present age of Ashwin’s son is equal to 10.

Note: There is an alternative method to solve this problem.
Let us assume
The age of Ashwin before 4 years = x.
The age of Ashwin’s son before 4 years =y.
From the question it is clear that 4 years ago, Ashwin was 6 times as old as his son.
\[x=6y......(1)\]
So,
The present age of Ashwin = x+4.
The present age of Ashwin’s son = y+4.
From the question, we are given that Ashwin’s age is four times his son’s present age.
\[\begin{align}
  & x+4=4(y+4) \\
 & \Rightarrow x+4=4y+16 \\
 & \Rightarrow x=4y+12.....(2) \\
\end{align}\]
Now we will substitute equation (1) and equation (2).
\[\begin{align}
  & 6y=4y+12 \\
 & \Rightarrow 2y=12 \\
 & \Rightarrow y=6......(3) \\
\end{align}\]
Now we will substitute equation (3) in equation (1).
\[\begin{align}
  & x=6(6) \\
 & \Rightarrow x=36....(4) \\
\end{align}\]
We know that the present age of Ashwin’s son is equal to (y+4).
\[\Rightarrow y+4=6+4=10\].
Hence, the present age of Ashwin’s son is equal to 10.