Question

four year ago age of a person was 9 times that of his son.four year later the age of the person will be four time the age of his son at that time find the present age of the person and his son​

Answer 1

Given :

• Four years age the age of a person was 9 times the age of his son.
• Four years later the age of that person will be four times the age of his son.

To find :

• Present age of son and that person

Solution :

Let,

• Present age of person = x years
• Present age of son = y years

Their ages 4 years ago were :-

→ Age of person = x - 4 years

→ Age of son = y - 4 years

According to the question,

→ Age of person = 9(Age of son)

→ x - 4 = 9(y - 4)

→ x - 4 = 9y - 36

→ x - 9y = - 36 + 4

→ x - 9y = - 32 ------(1)

Their ages after 4 years :-

→ Age of person = x + 4 years

→ Age of son = y + 4 years

According to the question,

→ Age of person = 4(Age of son)

→ x + 4 = 4(y + 4)

→ x + 4 = 4y + 16

→ x - 4y = 16 - 4

→ x - 4y = 12 -----(2)

Solving (1) and (2) :-

⠀⠀⠀⠀⠀⠀⠀⠀x - 9y = - 32

⠀⠀⠀⠀⠀⠀⠀⠀x - 4y = 12

⠀⠀⠀⠀⠀⠀⠀⠀(-)⠀(+)⠀(-)

⠀⠀⠀⠀⠀⠀_______________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀- 5y = - 44

⠀⠀⠀⠀⠀⠀________________⠀⠀

→ - 5y = - 44

→ y = 44/5

→ y = 8.8

Substituting the value of y in equation (1) :-

→ x - 9y = - 32

→ x - 9(8.8) = - 32

→ x - 79.2 = - 32

→ x = - 32 + 79.2

→ x = 47.2

Therefore,

• The present age of son = y = 8.8 years
• The present age of person = x = 47.2 years