To find present ages of father and son in a problem

Q. At present a father is 4 times as old as his son. After 5 year the sum of their ages will be 55. Find their present ages?

Solution:

Let F be the father's present age and S be the son's present age. 

Now solving the problem according to the given conditions in the problem:

1. At present:

F = 4S  _____________ eqn (1)

2. Five years after from now:

( F + 5 ) + ( S + 5) = 55

or (simplifying)

( F +  S + 10 = 55

F + S = 55 - 10

or

F + S = 45 _____________ eqn (2)

By substitution method, putting eqn (1) in eqn (2) to get age of son (S):

F + S = 45 

or (simplifying)

⇒    4S + S = 45 

⇒    5S =  45

⇒    S = 9 Years

Then, by putting the value of S=10 in any expressions (1) 0r (2) we get the mother age F:

Let in eqn (1)

F = 4S = 4(9) = 36 years

The present ages are

⇒ Father: 40 years.

⇒ Son: 10 years.

<Note: You Check (verify) both expressions putting the value of F and S. >

Method No. 2:

Solving the problem according to the given conditions:

Let the present age of the son be x, and the father's present age is 4x

After 5 years,

( x + 5 ) + ( 4x + 5) = 55

⇒    5x + 10 = 55

⇒    5x = 55 - 10

⇒    5x = 45

⇒    x = 9 

Thus,

- Son's present age = 9 years.

- Father's present age = 4x = 4 (9) = 36 years.