Question

One year ago, the father was 8 times as old as his son. Now his age is the square of his son’s age. Find their present ages.
A. Present age of a father is 36 years and that of his son is 6 years.
B. Present age of father is 49 years and that of his son is 7 years.
C. Present age of father is 64 years and that of his son is 8 years.
D. Present age of father is 25 years and that of his son is 5 years.

Answer 1

Hint: Take the father’s age as x and son’s age as y. Find the relations or equations according to the given conditions between x and y, solve them and get the answers.

Complete step-by-step answer:
In the question, we have been given the age relation between the father and son. We have been told that one year ago, the father was 8 times as old as his son and at present, the father’s age is the square of his son’s age. Now, using the given conditions, we will find the values of the father’s and son’s ages and hence solve the question.
Let us take the age of the father as x years and that of the son as y years. Now, considering condition 1, we get the age of the father as $x-1$ and the age of the son as $y-1$, so we can write it as,
$x-1=8\left( y-1 \right)$
Simplifying, we get,
$x-1=8y-8$
Adding 1 to both the side we get,
$x=8y-7$
Now applying the second condition, we can say the age of the father is x and that the age of the son is y, so we can write it as,
$x={{y}^{2}}$
From the first condition, we know that $x=8y-7$ so, substituting it, we get,
${{y}^{2}}=8y-7$
Now, taking $\left( 8y-7 \right)$ from the right hand side to the left, we get,
${{y}^{2}}-8y+7=0$
Splitting the middle term, we get,
${{y}^{2}}-y-7y+7=0$
On factorising it, we get,
$\left( y-1 \right)\left( y-7 \right)=0$
Hence the possible values of y will be 1 and 7. The value of 1 years is not possible as it does not satisfy any of the conditions. So, y or the age of the son will be 7 years. Then x or the age of the father will be ${{7}^{2}}=49$ years.
Hence option B is the correct answer.

Note: The students should read these kinds of problems carefully twice to avoid any mistakes. They should be careful while forming the equations and solving them. Instead of solving the question, one can also try considering the options given in the question, and then from those values try solving backwards and see which option satisfies the conditions.