Question

Four years ago, the father's age was three times the age of his son. the total of the age of the father and the son after 4 years will be 64 years. What is the father's age at present?
(a). 32 years
(b). 36 years
(c ). 44 years
(d). 40 years

Answer 1

Hint: For solving this problem, let the age of father be x and the age of son be y. Now, we form the first equation by using the information four years ago, the age of the father was three times the age of the son. Another equation was formed by using the second part of the statement. Since we have two variables and two equations, we can easily obtain father's age.

Complete step-by-step solution -
Let the age of father be x in years at present and the age of son be y in years at present.
Four years ago, the age of father was three times the age of son, so equation (1) will be
$\begin{align}
  & x-4=3(y-4) \\
 & x-4=3y-12 \\
 & x=3y-12+4 \\
 & x=3y-8\ldots (1) \\
\end{align}$
Now, after four years the total sum of ages of father and son will be 64 years. By using this fact, the equation (2) will be
$\begin{align}
  & x+4+y+4=64 \\
 & x+y=64-8 \\
 & x+y=56\ldots (2) \\
\end{align}$
Putting the value of x from equation (1) into equation (2), we get
$\begin{align}
  & 3y-8+y=56 \\
 & 4y=56+8 \\
 & 4y=64 \\
 & y=\dfrac{64}{4} \\
 & y=16 \\
\end{align}$
Substituting the value of y in equation (1), we get
$\begin{align}
  & x=3y-8 \\
 & x=3\times 16-8 \\
 & x=48-8 \\
 & x=40 \\
\end{align}$
Therefore, the age of father at present is 40 years.
Hence, option (d) is correct.

Note: The key concept involved in solving this problem is the interpretation of the problem statement into suitable equations to evaluate the variable. We can directly substitute y in the form of x to obtain the age of father without showing the age of son as only father’s age is required. This method will save time and effort.