Question

I am three times as old as my son's age . Five years later ,I shall be two and half times as old as my son. How old am I and my son?

Answer 1

I am three times as old as my son's age

Let, My son's age present age be $x$.

$\Rightarrow$ My age $=3x$.

Five years later,

My son's age $=x+5$

My age $=3x+5$

Five years later ,I shall be two and half times as old as my son

$\Rightarrow 3x+5=2\frac{1}{2}(x+5)$

$\Rightarrow 3x+5=\frac{5}{2}(x+5)$

$\Rightarrow 2(3x+5)=5(x+5)$

$\Rightarrow 6x+10=5x+25$

$\Rightarrow 6x-5x=25-10$

$\Rightarrow x=15$ ---(1)

$\Rightarrow 3x=3\times 15=45$ ---(2)

Hence, my age and son's age are $45$ years and $15$ years.