Question

Two years ago, father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Find their presents ages.

Answer 1

Step 1: Analyzing the given data:

Let us consider

Son’s present age be $=x$

Two years ago son’s age $=x–2$

His Father’s age at that time $=3(x–2)$

Present age of Father$=3x–6+2$

$=3x–4$

Two years hence father’s age $=3x–4+2$

Two years hence father’s age $=3x–2$

Two years hence son’s age $=x+2$

Step 2: Finding the value of $x$.

Now, according to the question

$\begin{array}{rcl}5\times (x+2)& =& 2(3x-2)\\ 5x+10& =& 6x-4\\ 6x-5x& =& 10+4\\ x& =& 14\end{array}$

Son’s present age $x=14years.$

Father’s present age $=(3\times 14)–4$$=38years$.

Hence, the present age of the son is $14years$ and the present age of the father is $38years$.