Question

I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. How old am I how old is my son.

Answer 1

Let the son's age be x.
Let my age be y.
=>y=3x [eq 1]
Five years later:-
=>y + 5 = 3x + 5
=>y + 5 = 5/2(3x+5)
=>y + 5 = 15x + 25 /2
=>>cross multiplacation
=>2(y+5) = 15x + 25
=>2y + 10 = 15x + 25
=>>Transverse the values
=>15x - 2y = 25 - 10
=>>Put the value of y from[eq 1]
=>15x - 2(3x) = 15
=>15x - 6x = 15
=>9x = 15
=>x = 15/9
=>x = 5/2
So,age of sun is 5/2 years.
=>>Now put the value of x in [eq 1]
=>y = 3 x 5/2
=>y = 15/2
So,my age will be 15/2 years.

Answer 2

$\textbf{ solution–}$

Suppose my age is x years and my son's age is y years.

Then
$x = 3y \: \: \: \: \: \: \: \: \: \: \: \: \: \: (i) (according. \: to \: ques.)$
Five years later,

My age will be ( x + 5 ) years and my son's age will be ( Y + 5 ) years.

$x + 5 = \frac{5}{2} (y + 5) \: \: \: \: \: \: \: \: \: \: \: \: \: \: |given| \\ 2(x + 5) = 5(y + 5) \\ 2x + 10 = 5y + 25 \\ 2x - 5y = 25 - 10 \\ 2x - 5y = 15 - - - - (ii)$

Putting (x=3y) in eq (ii)

$2x - 5y = 15 \\ 2 \times 3y - 5y = 15 \\ 6y - 5y = 15 \\ y = 15$

Put the value of y=15 in eq(i)

$x = 3y \\ x = 3 \times 15 \\ x = 45$

$\textbf{So, my present age is 45 years and}$
$\textbf{my son's present age is 15 years.}$
$\textbf{ Here my regarded to parents}$