Question

Two years ago , father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son . Find their present ages.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

${\huge{\underline{\underline{\sf{\blue{Question :-}}}}}}$

Two years ago , father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son . Find their present ages.

${\huge{\underline{\underline{\sf{\blue{Solution :-}}}}}}$

Hence,

Let Father's son's age 2 years ago = x years

Then, Father's age 2 years ago = 3x years

Therefore,

Father's present age = ( 3x + 2 ) years

Son's present age = ( x + 2 ) years

After 2 years from now , sons age

= ( x + 4 ) years

and Father's age = ( 3x + 4 ) years

${\huge{\underline{\underline{\sf{\blue{ATQ :-}}}}}}$

2 ( 3x + 4 ) = 5 (x + 4 )

=> 6x + 8 = 5x + 20

=> 6x - 5x = 20 - 8

i.e., x = 12

So, Father's son's present age = 12 + 2 = 14 years

And Father's present age = (3 × 12 + 2 ) = 38 years

Check : 2 years ago ,

Age of the son = (14 - 2) years = 12 years

Age of the Father = (38 - 2) = 36 years

And, 36 = 3 × 12 ( first condition )

2 years hence ,

Age of the son = (14 + 2) years = 16 years = 16 years

Age of the father = 38 + 2 = 40 years

And , 2 × 40 = 5 × 16 ( second condition)

80 = 80