Question

solve this problem ​

Answer 1

$\bold{Given}$

Sum of ages of two friends = 23

So, let the age of one friend be x so other will be (23 -x).

ACCORDING TO QUESTION

For Five years prior ,

Age of first friend = (x - 5)

Age of second friend= (23 - x - 5)

= (18 -x)

and product of there ages was 42 so,

$\mathsf{(x - 5)( 18 - x) = 42}$

On multiplying,

$\mathsf{18x - x^{2} - 90 + 5x= 42}$

$\mathsf{18x + 5x - x^{2} - 90 = 42}$

$\mathsf{23x - x^{2} - 90 = 42}$

On taking it to the other side,

$\mathsf{ 0= x^{2} - 23x + 90 + 42}$

$\mathsf{ 0= x^{2} - 23x + 132}$

On solving the following quadratic equation ,

$\mathsf{ 0= x^{2} - 11x - 12x + 132}$

$\mathsf{ 0= x(x - 11) - 12(x - 11)}$

$\mathsf{ 0= (x - 11)(x - 12)}$

On taking seperately,

$\mathsf{x - 11 = 0}$

$\boxed{\mathsf{x = 11}}$

$\mathsf{x - 12 = 0}$

$\boxed{\mathsf{x = 12}}$

So, the real or present ages of two friends is 11 years and 12 years or 12 years and 11 years.

So, after 5 years or 5 years hence tbere ages will be,

$\mathsf{11 + 5 = 16 \: years }$

$\mathsf{12 + 5 = 17 \: years}$