Question

The sum of the ages of
father and son is 45yrs.
Five years ago the
product of their ages
was 4 times the father's
age at that time the
present ages of father &
son are ?​

Answer 1

Answer:

the age of father is 39 years and the age of son is 6 years

Answer 2

$\huge \boxed{ \fcolorbox{cyan}{white}{Answer : }}$

$\rm{Let \: the \: age \: of \: father \: be \: x \: years}$

$\rm{age \: of \: his \: son \: be ( 45 - x ) years}$

$\star \sf \red{Five \: years \: ago}$

$\sf \pink{Age \: of \: father = ( x - 5 ) years}$

$\sf \pink{Age \: of \: his \: son = ( 45 - x - 5 ) years = ( 40 - x ) years}$

so from the question

product of their ages 5 years ago = 4×fathers ages five years ago

$\sf \blue{( x - 5 ) ( 40 - x ) = 4( x - 5 )}$

$\sf \blue{(x - 5)(40 - x) = 4(x - 5)}$

$\sf \blue{40 - x = 4}$

$\sf \blue{40 - 4 = x}$

$\sf \blue{36 = x}$

so..

$\sf \red{present \: of \: age \: of \: father}$

$\sf \red{ = xyears = 36yrs}$

$\star \rm \green{present \: age \: of \: his \: son}$

$\rm \green{(45 - x) =(45 - 36)}$