Question

Five years ago, the father was 7 times that of his son. At present time, the father’s age is 4 times that of his son. Find the present age of son and father?

Answer 1

Hint: We will assume the present age of son as x and fathers age as y. Then, using the circumstances in the question as a guide, create equations and solve these using a substitution method.

Complete step by step answer:
 We have given in present fathers age is 7 times that of son,
so, the equation is
$y = 4x$ --- (1)
Now, we will use the relations which is for 5 years ago
We have given that 5 years ago, fathers age is 7 times that of son.
So, the son’s age $ = x - 5$
and, the father’s age $ = y - 5$
the equation for their age 5 years ago
$ \Rightarrow y - 5 = 7(x - 5)$ --- (2)
We will know substitute the value of y from equation 1,
$ \Rightarrow 4x - 5 = 7(x - 5)$
$ \Rightarrow 4x - 5 = 7x - 35$
We have subtracted 4x and added 35 from both sides
$ \Rightarrow 35 - 5 = 7x - 4x$
$ \Rightarrow 30 = 3x$
$ \Rightarrow 10 = x$
We will find the present age of father using the equation 1
Present age of father, $y = 40$
Hence, the present age of the son is 10 and that of the father is 40.

Note:
If we just have one individual, we can simply answer age problems by choosing one variable and creating an equation using the provided condition. If there are two persons, we assign one variable to one of them and the second variable to the other, and then use the conditions in the question to create equations.
After creating the equations we can use the elimination method as well to get the result.