Question

A man is five times as old as his son. Four years ago the man was thirteen times as old as his son.

Find their present ages.

Answer 1

Age of son = 6 years

Age of man = 5×6 = 30 years

Explanation:

GIVEN :-

• A man is 5 times as old as his son. (In Present)
• 4 years ago , the man was 13 times as old as his son

TO FIND :-

• The present ages of the man & his son.

SOLUTION :-

Let the present age of son be 'x'.

⇒ Present age of man = 5x

4 years ago ,

Age of son = (Present age of son) - 4 = x - 4

Age of man = (Present age of man) - 4 = 5x - 4

The man was thirteen times as old as his son. So,

`=> 5x - 4 = 13(x - 4)`

Now , solve the equation.

• Open the brackets in R.H.S.

`=> 5x - 4 = 13x - 52`

• Take 5x to R.H.S. and -52 to L.H.S. Also , take care of their signs because they are getting displaced from L.H.S. to R.H.S. or vice-versa.

`=> 13x - 5x = 52 - 4`

`=> 8x = 48`

• Divide both the sides by 8

`=> (8x)/(8) = (48)/(8)`

`=> x = 6`

CONCLUSION :-

Age of son = 6 years

Age of man = 5×6 = 30 years