Question

3 years ago, the sum of the ages of a father and his son was 40 years. After 2 years the sum of age of father and son will be____________.
(a) 40
(b) 46
(c) 50
(d) 60

Answer 1

Hint: Let present age of father be x and present age of son be y. Sum of the age of father and son three years ago is mentioned so we will go back and then from the given details in the question we will solve this problem.

Complete step-by-step answer:

Let the present age of father be x and present age of son be y.
It is mentioned in the question that three years ago, the sum of ages of father and son was 40.
So the age of the father 3 years ago was \[x-3\] years, and the age of the son three years ago was \[y-3\] years.
Using these information, we get,
 \[\Rightarrow (x-3)+(y-3)=40........(1)\]
Rearranging equation (1) we get,
 \[\begin{align}
  & \,\Rightarrow x+y=40+6 \\
 & \,\Rightarrow x+y=46 \\
 & \,\Rightarrow y=46-x........(2) \\
\end{align}\]
In the question it has been asked to find the sum of age of father and son after 2 years, so let this sum be t.
So age of father after two years will be \[x+2\] years, and age of son after two years will be
\[y+2\] years.
Using these information, we get,
 \[\,\Rightarrow t=(x+2)+(y+2)........(3)\]
Now substituting value of y from equation (2) in equation (3) we get,
 \[\,\Rightarrow t=(x+2)+(46-x+2)........(4)\]
Now cancelling similar terms from equation (4) and solving we get,
 \[\,\Rightarrow t=2+46+2=50\]
So the answer is that the sum of the age of father and son after 2 years is 50 years. Hence option (c) is the right answer.

Note: Here we are taking the present age of father and son to be x and y because this technique consumes less time. Grasping these types of questions in one go is difficult so we will try to read it 3 to 4 times and then proceed with the solution.