Question

• Two years ago, father was three times as old as
his son and two years hence, twis his age will
be equal to 5 times that of his son find their
present ages.​

Answer 1

Given :-  

• Two years ago, father was three times as old as his son and two years hence, twice his age will be equal to 5 times that of his son.  

To Find :-

• Find their present ages

Solution :-

~Let the present age of the son be ‘x’  

Two years ago –

Son’s age :

• ( x - 2 ) years  

Father’s age :

⇒  3( x - 2 )  

• ( 3x - 6 ) years

Present ages –

Son’s age :

• ( x ) years

Father’s age :

⇒ ( 3x - 6 ) + 2  

⇒ 3x - 6 + 2  

• ( 3x -4 ) years  

Two years hence –

Son’s age :

• ( x + 2 ) years  

Father’s age :

⇒ ( 3x - 4 ) + 2  

⇒ 3x - 4 + 2  

• ( 3x - 2 ) years  

According to the question :-

⟶ 5( x + 2 ) = 2( 3x -2 )  

⟶ 5x + 10 = 6x -4  

⟶ 6x -5x = 10 + 4  

⟶ x = 14  

Finding their present ages :-

Son’s age :

• x = 14 years  

Father’s age :

⇒ ( 3x - 4 )  

⇒ ( 3 × 14 - 4 )  

⇒ 42 - 4  

• 38 years  

Hence,  

• Present age of the son is 14 years and father is 38 years  

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Answer 2

•Given-

☞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.

•To find-

☞ Present age of father and son

•Solution-

• Let the present age of the son be 'x'

☆Two years ago:

•Son's age - ( x - 2 ) years

•Father's age - 3 ( x - 2 )

      = (3x - 6) years

☆Present age -

• Son's age = (x) years

• Father's age = (3x - 6) + 2

         = 3x - 6 + 2

         = (3x - 4) years

•Two years hence -

➜ Son's age - (x + 2) years

➜ Father's age - (3x - 4) + 2

       - 3x - 4 + 2

       - (3x - 2) years

❥According to the question -

➜ 5 (x + 2) = 2 (3x - 2)

➜5x + 10 = 6x - 4

➜6x - 5x = 10 + 4

➜x = 14

    _______________

•Son's age = x = 14 years

•Father's age = (3x - 4)

      = (3 x 14 - 4)

      = (42 - 4)

      = 38 years

Hence,

☞ The present age of Son is 14 and Father is 38.

     _____________