Question

By adding one-third the age of Salim’s father before 5 years to half of the present age of his father we get 20, then find the present age of Salim’s father.

Answer 1

Hint: We solve this problem by assuming the present age of Salim’s father as a variable. Then we use the given condition that is adding one third the age of Salim’s father before 5 years to half of the age of his father we get 20 to form a mathematical equation to solve for the variable we assumed to get the required answer.

Complete step-by-step solution
Let us assume that the present age of Salim’s father as \['x'\]
We are given that adding one third age of Salim’s father before 5 years to the half of the age of his father we get 20
We know that if the present age of a person if \['x'\] then the age before five years will be \[x-5\]
Let us assume that the one third of age of Salim’s father before five years as \[B\] then we get
\[\begin{align}
  & \Rightarrow B=\dfrac{1}{3}\left( x-5 \right) \\
 & \Rightarrow B=\dfrac{x-5}{3} \\
\end{align}\]
Now, let us assume that the half of present age of Salim’s father as \[A\] then we get
\[\begin{align}
  & \Rightarrow A=\dfrac{1}{2}\left( x \right) \\
 & \Rightarrow A=\dfrac{x}{2} \\
\end{align}\]
Now, by converting the given statement to mathematical equation we get
\[\Rightarrow B+A=20\]
By substituting the required values in above we get
\[\Rightarrow \dfrac{x-5}{3}+\dfrac{x}{2}=20\]
Now, by adding the terms using the LCM form we get
\[\begin{align}
  & \Rightarrow \dfrac{2x-10+3x}{6}=20 \\
 & \Rightarrow 5x=120+10 \\
 & \Rightarrow x=26 \\
\end{align}\]
Therefore, we can say the present age of Salim’s father is 26 years.

Note: Students may do mistake in the first part that is we have the present age of Salim’s father as \['x'\] then the age before 5 years is given as \[x-5\]
So, we have the value of one third of age of Salim’s father before five years as
\[\begin{align}
  & \Rightarrow B=\dfrac{1}{3}\left( x-5 \right) \\
 & \Rightarrow B=\dfrac{x-5}{3} \\
\end{align}\]
But students may miss this par that is the age before 5 years is given as \[x-5\] and take the above equation as
\[\begin{align}
  & \Rightarrow B=\dfrac{1}{3}\left( x \right) \\
 & \Rightarrow B=\dfrac{x}{3} \\
\end{align}\]
This gives the wrong answer.