Question

four years ago,my father's age was 4times that of my age.At present the sum of my father's age and that of mine is 53 years,what are our present ages?​

Answer 1

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Answer 2

GIVEN :-

• Four years ago father's age was four times his son's age.
• At present sum of their ages is 53 .

TO FIND :-

• Present age of father .
• Present age of son .

SOLUTION :-

    Let ,

• Present age of son = x
• Present age of father = y

     Four years ago ,

• Age of son = x - 4
• Age of father  = y - 4

     According to the first condition ,

       $\longrightarrow \sf 4(x-4)= y-4\\\\\longrightarrow 4x - 16=y-4\\\\\longrightarrow 4x -y = 12 \ \ \ \ \ \ \ \ \ \ \ \ ..............(1)$

    According to the second condition ,

        $\longrightarrow \sf x + y = 53 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

    Add Eq (1) and Eq (2) ,

        $\longrightarrow 5x = 65\\\\\longrightarrow \bf x = 13$

   

  Put the value of x in Eq (2) ,

       

      $\longrightarrow \sf 13+y = 53\\\\\longrightarrow y = 40$

  ➤ Present age of son = 13 years

  ➤ Present age of father = 40 years