Question

five years ago a man was seven times as old as his son . five years hence the father will be three times as old as his son.find their present ages

Answer 1

Hey !



Let present age of father and son be X and Y.




Five years ago age of father = Present age - 5 = ( X - 5 ) years.



Five years aoe age of son = Present age - 5 = ( Y - 5).




A/Q,



Age of father before 5 years = 7 ( Age of son before 5 years ).





X - 5 = 7 ( Y - 5 )



X - 5 = 7Y - 35



X - 7Y = -35 + 5



X - 7Y = -30 -----------(1)




Five years hence age of father = ( X + 5 ) years.



Five years hence age of son = ( Y + 5 ) years.


A/Q





X + 5 = 3 ( Y + 5 )



X + 5 = 3Y + 15



X - 3Y = 10 --------(2)



From (2) , we get



X - 3Y = 10


X = ( 10 + 3Y ) -----(3)



Putting the value of x in (1)

X - 7Y = -30



10 + 3Y - 7Y = -30



-4Y = -40



Y = 10 years.


Putting the value of Y in (3)



X = 10 + 3Y


X = 40 years.


Father age = 40 years.

and,

son age = 10 years.