Question

five years ago,a man was seven times as old as his son , while five year hence , the man will be four times as old as his son . find their present age

Answer 1

let the age of sun be x.
7(x-5) = x-5.
4(x+5) = x+5 ,

Answer 2

Answer:

The present ages of man and son are 155 years and 35 years respectively.

Step-by-step-explanation:

Let the present age of son be x years.

And the present age of man be y years.

Age of son five years ago = ( x - 5 ) years

Age of man five years ago = ( y - 5 ) years

From the first condition,

The man was 7 times as old as his son five years ago.

∴ 5 ( x - 5 ) = y - 5

⇒ 5x - 25 = y - 5

⇒ 5x = y - 5 + 25

⇒ 5x = y + 20

⇒ x = ( y + 20 ) / 5 - - - ( 1 )

Now,

Age of son five years hence = ( x + 5 ) years

Age of man five years hence = ( y + 5 ) years

From the second condition,

The man will be 4 times as old as his son five years hence.

∴ 4 ( x + 5 ) = y + 5

⇒ 4x + 20 = y + 5

⇒ 4x - y = 5 - 20

⇒ [ 4 ( y + 20 ) / 5 ] - y = - 15 - - - [ From ( 1 ) ]

⇒ [ ( 4y + 80 ) / 5 ] - y = - 15

⇒ ( 4y + 80 - 5y ) / 5 = - 15

⇒ 4y - 5y + 80 = - 15 * 5

⇒ - y + 80 = - 75

⇒ - y = - 75 - 80

⇒ - y = - 155

⇒ y = 155

Present age of man = 155 years

By substituting y = 155 in equation ( 1 ),

x = ( y + 20 ) / 5 - - - ( 1 )

⇒ x = ( 155 + 20 ) / 5

⇒ x = 175 / 5

⇒ x = 35

Present age of son = 35 years

The present ages of man and son are 155 years and 35 years respectively.