Question

45) Aftab tells his daughter, Seven years ago, I was seven times as old as you were then. Also,
three years from now. I shall be three times as old as you will be. Find their present ages.​

Answer 1

Answer:

The present ages of Aftab and his daughter are 42 and 12 years respectively.

Step-by-step explanation:

Given :

Seven years ago = Aftab was seven timed old as his daughter

3 years after the present time = Aftab would be twice as old as his daughter

To find :

Their present ages

Solution :

$\textbf{\small{\underline{Let the age 7 years back be -}}}$

• His daughter as y
• Aftab's age as 7y

$\textbf{\small{\underline{Present ages - }}}$

• His daughter = (y + 7)
• Aftab = (7y + 7)

$\textbf{\small{\underline{Ages 3 years hence from present -}}}$

• Daughter = (y + 7) + 3
• Aftab = (7y + 7) + 3

$\textbf{\small{\underline{According to the Question - }}}$

3 years after the present time = Aftab would be twice as old as his daughter

⇒ (7y + 7) + 3 = 3(y + 7 + 3)

⇒ 7y + 10 = 3(y + 10)

⇒ 7y + 10 = 3y + 30

⇒ 7y - 3y = 30 - 10

⇒ 4y = 20

⇒ y = 20/4

⇒ y = 5

$\rule{300}{1.5}$

★ $\textsf{Value of (y + 7) }$

⇒ 5 + 7

⇒ 12

$\textsf{His daughter is 12 years old.}$

$\rule{300}{1.5}$

★ $\textsf{Value of 7y + 7}$

⇒ 7(5) + 7

⇒ 35 + 7

⇒ 42

$\textsf{Aftab is 42 years old.}$

$\therefore$ The present ages of Aftab and his daughter are 42 and 12 years respectively.

Answer 2

Answer :

Age of Aftab is 42 and his daughter's age is 12.

Step-by-step explanation:

Assume the ages of father (Aftab) and his daughter be x and y respectively.

It is Given that the age of aftab was seven times the age of her daughter seven years ago.

• Ages before 7 years :

Aftab = x - 7

Daughter = y - 7

∵ the age of father was seven times the age of daughter -

x - 7 = 7(y - 7)

x - 7 = 7y - 49

x = 7y - 49 + 7

x = 7y - 42 ___[ eq. I]

Now,

Also, after 3 years the age of father will be three times the age of daughter.

• Their ages after 3 years :

x + 3 ____( Father )

y + 3 ____(Daughter)

(x + 3) = (y +3)3 _____[ eq. ii]

By substituting the value of eq. I in eq ii :

(x + 3) = (y +3)3

7y - 42 + 3 = 3y + 9

7y - 3y = 39 + 9

4y = 48

y = 12

Age of (y) Daughter = 12

and the age of her (x) father :

x = 7y - 42

x = 84 - 42

x = 42.

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