Question

The sum of the ages of a father and his son is 50 years. Five years ago the product of their ages was 175. Find their present ages .........

Answer 1

Hi Mate !!


Let the present age of father be x
and the present age of son be y

• The sum of the ages of a father and his son is 50 years

x + y = 50

x = 50 - y ........ ( i )

• Five Years ago their age will be

Father's age :- ( x - 5 ) years
Son's age :- ( y - 5 ) years

° Five years ago the product of their ages was 175.

( x - 5 ) ( y - 5 ) = 175

xy - 5x - 5y + 25 = 175

xy - 5x - 5y = 175 - 25

xy - 5x - 5y = 150 .... ( ii )


Putting value of x from ( i ) in ( ii )

xy - 5x - 5y = 150

( 50 - y ) y - 5 ( 50 - y ) - 5y = 150

50y - y² - 250 + 5y - 5y = 150

- y² + 50y - 250 = 150

- y² + 50y = 150 + 250

- y² + 50y = 400

y² - 50y + 400 = 0

y² - 40y - 10y + 400 = 0

y ( y - 40 ) - 10 ( y - 40 ) = 0

( y - 10 ) ( y - 40 ) = 0


• ( y - 10 ) = 0

y = 10

• ( y - 40 ) = 0

y = 40
[ neglected as the age of Son can't be more than his own father ]


Putting the value of y as 10 in the ( i ) Equation

x = 50 - y

x = 50 - 10

x = 40


So,
the present age of Father is ( x ) :- 40 years
and the present age of son is ( y ) :- 10years