The son’s age is one-third that of his father. Five years ago father’s age was 4 times as old as his son. Find their present age.<

2 thoughts on “The son’s age is one-third that of his father. Five years ago father’s age was 4 times as old as his son. Find their present age.<”

1. Answer:

   let the present age of son be x

   son’s age is one – third of his father’s age =

   y=x —- (1)

   3

   5yrs ago father’s age was 4 times of his sons age

   y= 4x-5 —(2)

   Step-by-step explanation:

   this is the equation we get

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2. Given:

   • Son’s age is ⅓ that of his father.
   • Five years ago, father’s age was 4 times his son’s age.

   To Find:

   • What are their present ages?

   Process:

   To find their present ages we will first let the father’s age be x. Then, son’s age will be x/3. Five years ago son’s age will be (x/3 – 5) and father’s age will be (x – 5). It is given father’s age was 4 times son’s age. So, we can form an equation as follows:

   • x – 5 = 4(x/3 – 5)

   After solving the equation to get the value of x, the value of x is equal to the age of the father and x/3 will be the age of the son.

   Solution:

   Let the father’s age be x.

   Then, the son’s age will be x/3.

   Five years ago:

   Son’s age = (x/3 – 5)

   Father’s age = (x – 5)

   ∵ Five years ago father’s age was 4 times his son’s age. [given]

   [tex]\therefore\sf{x-5=4\bigg(\dfrac{x}{3}-5\bigg)}[/tex]

   [tex]\implies\sf{x-5=\dfrac{4x}{3}-20}[/tex]

   [tex]\implies\sf{x-\dfrac{4x}{3} = 5-20}[/tex]

   [tex]\implies\sf{\dfrac{3x-4x}{3}=-15}[/tex]

   [tex]\implies\sf{\dfrac{-x}{3}=-15}[/tex]

   [tex]\implies\sf{-x=-15\times3}[/tex]

   [tex]\implies\sf{\not\!\!{-}x=\not\!\!{-}45}[/tex]

   [tex]\implies\sf{x = 45}[/tex]

   Hence, value of x is 45.

   Therefore, father’s age = x = 45 years

   And son’s age = x/3 = 45/3 = 15 years

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