Question

If the sum of the ages of a father and his son in years is 65 and twice the difference of their ages in years is 50, then the age of the father is,
A. 45 years
B. 40 years
C. 50 years
D. 55 years

Answer 1

Hint: In the provided question, we will have to assume the age of the father and son to be some variable, let us say x and y respectively as the ages of the father and son. So, according to the question, the first equation that we can form will be $x+y=65$. Similarly, we will form the second equation as $2\left( x-y \right)=50$. We will then perform the mathematical operations on these two equations using the elimination method, which will leave us with the value of x, which is the age of the father.

 Complete step-by-step solution:
Let us assume the age of the father as x and the age of his son as y. We are given that the sum of their age is 65, which implies that,
Age of father + age of son = 65
$\Rightarrow x+y=65\ldots \ldots \ldots \left( i \right)$
We are also given that twice the difference of their age is 50. Therefore, it implies that,
2 (Age of the father - age of the son) = 50
$\begin{align}
  & \Rightarrow 2\left( x-y \right)=50 \\
 & \Rightarrow \left( x-y \right)=\dfrac{50}{2} \\
 & \Rightarrow \left( x-y \right)=25\ldots \ldots \ldots \left( ii \right) \\
\end{align}$
We will now add equation (i) and (ii) to get the value of x. So, adding the two equations, we will get,
$\begin{align}
  & x+y+x-y=65+25 \\
 & \Rightarrow 2x=90 \\
 & \Rightarrow x=\dfrac{90}{2} \\
 & \Rightarrow x=45 \\
\end{align}$
Therefore, we get the value of x as 45, which means the age of the father is 45 years.
Hence the correct answer is option A.

Note: The students can possibly go wrong in this question by using the substituting method, where they might substitute the value of x in terms of y from one equation to the second equation which will give us the value of y, and then we can put that value in any one of the equations to get the value of x. This process will give us the right answer too, but it will make the solution lengthy, so we can simply use the elimination method as our goal is to find the age of the father only, that is x.