Question

After fifteen years Ali will be twice as old as his son
but five years ago he was he was four-times as old as
his son their present ages are?
A) 15,45
B) 17,51
C) 13,39
D) 16,48
A is the ans all I need is solution guys.right ans get brainliest​

Answer 1

Given

• Ali's age after 15 years = Twice the age of his son.
• Ali's age before 5 years = 4 times his son's age.

To find

• Present age of Ali and his son.

Solution

Let the present age of Ali be x years and his son's age be y years.

As given in the question,

After 15 years their ages will be :-

• Ali's age = x + 15 years
• His son's age = y + 15 years

Now, according to the question.

⟼ x + 15 = 2(y + 15) ---(1) [Eqn. 1]

As given in the question,

5 years ago their ages were :-

• Ali's age = x - 5 years
• His son's age = y - 5 years

Now, according to the question.

⟼ x - 5 = 4(y - 5) ---(2) [Eqn. 2]

________________________

Taking Eqn. 1 :-

⟼ x + 15 = 2(y + 15)

⟼ x + 15 = 2y + 30

⟼ x - 2y = 30 - 15

⟼ x - 2y = 15 ---(3)

Taking Eqn. 2 :-

⟼ x - 5 = 4(y - 5)

⟼ x - 5 = 4y - 20

⟼ x - 4y = - 20 + 5

⟼ x - 4y = - 15 ---(4)

Solving (3) and (4)

x - 2y = 15

x - 4y = - 15

- + +

___________

+ 2y = 30

____________

⟼ 2y = 30

⟼ y = 30/2

⟼ y = 15

The value of y = 15.

Substitute the value of y in (1)

[Note. Here I have substituted the value of y in eqn. 1, while solving you can substitute it in any equation.]

⟼ x + 15 = 2(y + 15)

⟼ x + 15 = 2(15 + 15)

⟼ x + 15 = 2(30)

⟼ x + 15 = 60

⟼ x = 60 - 15

⟼ x = 45

∴ The value of x = 45.

The present ages of Ali and his son :-

• Ali's age = x = 45 years.
• His son's age = y = 15 years.

Answer ⟼ Option (a) 15, 45.