Question

3 years ago, the sum of the ages of a father and his son was 40 years. What will be the sum of the age of father and son after 2 years?

Answer 1

Hint: Here, first we have to consider the age of father as x and age of son as y. Before three years the sum of their ages was 40, hence we will get the equation:
$x-3+y-3=40$
Now, sum of ages of father and son after two years is:
$s=x+2+y+2$
Next, by solving the two equations we will get the answer.

Complete step by step answer:
We are given that 3 years ago the sum of the ages of father and his son was 40 years.
Now, we have to find the sum of the age of father and son after 2 years.
First, let us consider the age of father be x and age of son be y.
Then, before three years we have:
Age of father = $x-3$
Age of son = $y-3$
We have that the sum of the ages of father and son before three years is 40. Therefore, we can write:
$\begin{align}
  & x-3+y-3=40 \\
 & x+y-6=40 \\
\end{align}$
In the next step, take -6 to the right side then -6 becomes 6. Hence, we will obtain:
$x+y=40+6$
$x+y=46$ ……. (1)
Now, let us consider the ages of father and son after two years. We will get:
Age of father after two years = $x+2$
 Age of son after two years = $y+2$
Next, let us take the sum of father and son after two years, we will obtain:
$s=x+2+y+2$
$s=x+y+4$ …… (2)
Now, by substituting equation (1) in equation (2), we obtain:
$\begin{align}
  & s=46+4 \\
 & s=50 \\
\end{align}$
Hence we got the sum as 50.
Therefore, we can say that the sum of ages of father and son after two years will be 50.

Note: Here, from the first condition you can also write the present ages of father as x and son as $46-x$. Now, after two years you can take the age as $x+2$ and $46-x+2$. Next, by adding these two ages you will get the sum.