Question

After five years, the age of a father will be thrice the age of his son. Five years ago, he was seven times old as his son was. What is father's present age?

Answer 1

Let the father's age be x and the son's age be y

 

Five years hence:

Father's age = x+5

Son's age = y+5

Given: x+5 = 3(y+5)

That is x - 3y = 10   ....(1)

 

Five years ago:

Father's age = x - 5

Son's age = y - 5

Given: x - 5 = 7(y - 5)

That is x - 7y = -30   ....(2)

 

Solving the two simultaneous equations we have

x = 40 and y = 10

 

Thus the present ages of father and son are 40 and 10

Answer 2

Given

• After 5 years, the age of a father will be thrice the age of his son.
• 5 years ago, he was seven times old as his son was.

Explanation:

Let the present age of the son be x Years

5 years ago, age of son be = (x - 5) Years

According to Question,

5 Years ago, Father's age = 7(x - 5) Years

$\huge{ \circ }$ After 5 Years :-

• Age of the son = (x - 5 + 10) Years
• Father's age = [7(x - 5) + 10] Years

According to the second condition in the Question,

• Father's age = 3( x-5+10)

Now, Arranging this Equations as:-

$\colon\implies{\sf{ 7(x-5)+10 = 3(x+5) }} \\ \\ \\ \colon\implies{\sf{ 7(x-5)+10 = 3(x+5) }} \\ \\ \\ \colon\implies{\sf{ 7x-35+10=3x+15}} \\ \\ \\ \colon\implies{\sf{ 7x - 3x = 15 + 35 - 10}} \\ \\ \\ \colon\implies{\sf{ \cancel{4} x = \cancel{40} }} \\ \\ \\ \colon\implies{\sf{ x = 10 }}$

Thus,

The Present Father's age :-

$\implies{\sf{ 7(x - 5) + 5}} \\ \\ \implies{\sf{ 7(10 - 5) + 5}} \\ \\ \implies{\sf{ 7 \times 5 + 5}} \\ \\ \implies{\sf{ 35 + 5 }} \\ \\ \implies{\boxed{\mathfrak\pink{ 40 }}}$

Hence,

• The Present age of the Father is 40 Years.