Question

The sum of father’s age and twice the age of his son is 70. If we double the age of the father and add it to the age of his son the sum is 95. Find their present ages.

Answer 1

Let the father's age be x years and son's age be y years. 

Sum of father’s age and twice the age of his son is 70 so,
x + 2y = 70                         ......(I)

Double the age of the father added to the age of his son the sum is 95.
2x + y = 95                        .....(II)

Adding (I) and (II), we get,
\[\begin{array}{l}  
\phantom{\texttt{0}}\texttt{ x + 2y = 70}\\
\phantom{\texttt{}}\texttt{+ 2x + y = 95}\\\hline \end{array}\]
∴ 3x + 3y = 165

Dividing by 3,
x + y = 55                        ...(III)

Subtracting (I) from (II),
\[\begin{array}{l}  
\phantom{\texttt{0}}\texttt{ x + 2y = 70}\\
\phantom{\texttt{}}\texttt{- 2x + y = 95}\\
\hline\phantom{\texttt{}}\texttt{ (-) (-) (-)}\\
\hline \end{array}\]
∴ − x + y = − 25
∴ x − y = 25                   ...(IV)

Adding (III) and (IV), we get,

\[\begin{array}{l}  
\phantom{\texttt{0}}\texttt{ x + y = 55}\\
\phantom{\texttt{}}\texttt{+ x − y = 25}\\\hline \end{array}\]
∴ 2x = 80

∴  x = 40
Putting the value of x = 40 in equation (III),
x + y = 55 
∴ 40 + y = 55
∴ y = 55 − 40
∴ y = 15

Thus, the age of the father is 40 years and age of his son is 15 years.