Question

Aditya’s father’s present age is five times his present age. Two years from now, Aditya’s age will be one fourth of his father’s age at the time. Find both Aditya’s and his father's present age.

Answer 1

Hint: Let us assume the age of Aditya is equal to y and the age of Aditya’s father is equal to x. From the question, it is clear that Aditya’s father’s present age is five times his present age. Now we should represent that above statement by obtaining a relation between x and y. Let us assume this equation as equation (1). From the question, it is clear that the age of Aditya after two years is one-fourth of his father’s age.
Complete step by step answer:
Let us assume Aditya’s age as y and his father’s age as x.
From the question, it was given that Aditya’s father’s present age is five times his present age.
So, we get
\[x=5y....(1)\]
Now we have to find the age of Aditya and the age of Aditya’s father.
Age of Aditya’s after 2 years \[=x+2\]
Age of Aditya’s father after 2 years \[=y+2\]
From the question, it was given that from the age of Aditya and the age of his father after 2 years.
\[y+2=\dfrac{x+2}{4}\]
By using cross multiplication, we get
\[\begin{align}
  & x+2=4(y+2) \\
 & \Rightarrow x+2=4y+8 \\
 & \Rightarrow x=4y+6....(2) \\
\end{align}\]
Now let us substitute equation (1) in equation (2), we get
 \[\begin{align}
  & \Rightarrow 5y=4y+6 \\
 & \Rightarrow y=6.....(3) \\
\end{align}\]
Now we will substitute equation (3) in equation (1).
\[\begin{align}
  & \Rightarrow x=4(6)+5 \\
 & \Rightarrow x=30.....(4) \\
\end{align}\]
So, from equation (3) it is clear that the age of Aditya is equal to 6.
So, from equation (4) it is clear that the age of Aditya’s father is equal to 30.

Note: Students may read the question in an incorrect and have a wrong answer at the end.
It was given from the age of Aditya and the age of his father after 2 years. If students write
\[\begin{align}
  & \Rightarrow x+2=\dfrac{y+2}{4} \\
 & \Rightarrow y+2=4(x+2) \\
 & \Rightarrow y=4x+6.....(5) \\
\end{align}\]
Now we will place equation (5) in equation (1), we get
\[\begin{align}
  & \Rightarrow x=5(4x+6) \\
 & \Rightarrow x=20x+30 \\
 & \Rightarrow -19x=30 \\
 & \Rightarrow x=\dfrac{-30}{19} \\
\end{align}\]
Now we get the age of Aditya’s father is equal to \[\dfrac{-30}{19}\] which is not possible. So, the question should be read carefully by the student.