Question

A father and his son decides to sum their ages. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be?

Answer 1

Answer :

20 years

Step-by-step explanation :

Let the present age of father be x years

and his son's present age be y years

Father and his son decides to sum their ages. The sum is equal to sixty years

Sum of their ages = 60 years

         x + y = 60

         x = 60 - y  -- eqn [1]

Six years ago,

father's age was = (x - 6) years

his son's age was = (y - 6) years

Given, Six years ago the age of the father was five times the age of the son

  x - 6 = 5(y - 6)

  x - 6 = 5y - 30

  5y - x = 30 - 6

  5y - x = 24

  5y - (60 - y) = 24  [ eqn. [1] ]

  5y - 60 + y = 24

   6y = 24 + 60

   6y = 84

    y = 84/6

    y = 14

The present age of son = 14 years

The present age of father = 60 - 14 = 46 years

After six years,

his son's age will be = 14 + 6 = 20 years

Verification :

Condition - 1 : The sum is equal to sixty years.

      14 + 46 = 60

         60 = 60

        LHS = RHS

Condition - 2 : Six years ago the age of the father was five times the age of the son.

Six years ago,

Father's age = 46 - 6 = 40 years

Son's age = 14 - 6 = 8 years

father's age = 5(son's age)

   40 = 5(8)

    40 = 40

   LHS = RHS

Hence proved!

Answer 2

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A father and his son decides to sum their ages. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be?

❇ Solution ⬇

Let the present age of father be x years

and his son's present age be y years

Father and his son decides to sum their ages. The sum is equal to sixty years

Sum of their ages = 60 years

         x + y = 60

         x = 60 - y  -- [1]

Six years ago,

father's age was = (x - 6) years

his son's age was = (y - 6) years

Given, Six years ago the age of the father was five times the age of the son

 

x - 6 = 5(y - 6)

x - 6 = 5y - 30

5y - x = 30 - 6

5y - x = 24

5y - (60 - y) = 24  [ eqn. [1] ]

5y - 60 + y = 24

6y = 24 + 60

6y = 84

y = 84/6

y = 14

Son's present age = 14 years

Father's present age = 60 - 14 = 46 years

After six years,

Son's age will be = 14 + 6 = 20 years

Thank you.