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Answer 1

(9)

Let, the present age of father is x years and that of his son is y years

By the given conditions,

x + 5 = 3 (y + 5)

⇒ x + 5 = 3y + 15

⇒ x = 3y + 10 .....(i)

x - 5 = 7 (y - 5)

⇒ 3y + 10 - 5 = 7y - 35 [ by (i) ]

⇒ 3y + 5 = 7y - 35

⇒ 7y - 3y = 5 + 35

⇒ 4y = 40

⇒ y = 10

Putting y = 10 in (i) no. equation, we get

x = 3 (10) + 10

⇒ x = 30 + 10

⇒ x = 40

Therefore, the present age of the father is 40 years and that of his son is 10 years.

(10)

Let, the present age of the father js x years and that of his son is y years

By the given conditions,

x - 1 = 8 (y - 1)

⇒ x - 1 = 8y - 8

⇒ x = 8y - 7 .....(i)

x = y²

⇒ 8y - 7 = y²

⇒ y² - 8y + 7 = 0

⇒ y² - y - 7y + 7 = 0

⇒ y (y - 1) - 7 (y - 1) = 0

⇒ (y - 1) (y - 7) = 0

Either y - 1 = 0 or, y - 7 = 0

⇒ y = 1 , y = 7

• Putting y = 1 in (i) no. equation, we get x = 8 (1) - 7 = 8 - 7 = 1
• Putting y = 7 in (i) no. equation, we get x = 8 (7) - 7 = 56 - 7 = 49

Since x = 1 looks inappropriate as the age of the father, we take x = 49

Therefore, the present age of the father is 49 years and that of the son is 7 years.

Answer 2

Heya!!

Let the present age of son be = x

And let the present age of his father be = y

ACCORDING TO THE GIVEN QUESTION!

y+5 = 3(x+5) ... Equation ( i )

FIVE YEARS AGO

y - 5 = 7 ( x - 5 ) ... Equation ( ii )

ADD BOTH THE EQUATIONS WE HAVE!

2y = 10x -20

y = 5x - 10

x = 10years.

y = 40years.

So, the present age of son is = 10years.

And

present age of his father is = 30years.