Question

the sum of my elder sisters present age and my father's age is 55 years by calculating.i observed that after 16 years,my father's age will be two times more than my sister's.


⭐simultaneous equations .....⭐

Answer 1

Hi there!
Here's the answer:

•°•°•°•°•°•<><><<><>><><>•°•°•°•°•°•

¶ Keep track on Present age while solving problems on Ages.

SOLUTION:

Let the present age of Father = 55 - x
Let present age of elder sister = x

{ °•° Given that the sum of their ages is 55 & x + (55-x) = 55 }

After 16 years,
The age of Father = (55 - x) +16 = 71 - x
The age of elder sister = x + 16

Given,
Father's age = 2 × ( Elder sister's age)
=> 71 - x = 2 × ( x + 16 )
=> 71 - x = 2x + 32
=> 3x = 71 - 32
=> 3x = 39
=> x = 13

•°• Present Age of Elder sister = x = 13

& Present Age of Father = 55-x
= 55 - 13
= 42

•°•°•°•°•°•<><><<><>><><>•°•°•°•°•°•

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:)

Hope it helps

Answer 2

Let the elder sister's present age = x.

Let the present age of father = y.

Given that sum of their ages = x + y = 55    ----- (1)

After 16 years:

⇒ Age of elder sister = x + 16.

⇒ Age of father = y + 16.

Given that after 16 years, my father's age will be two times more than sisters age.

⇒ y + 16 = 2(x + 16)

⇒ y + 16 = 2x + 32

⇒ y - 2x = 16

⇒ 2x - y = -16

On solving (1) & (2), we get

⇒ x + y = 55

⇒ 2x - y = -16

   ----------------

         3x = 39

           x = 13.

Substitute x = 13 in (1), we get

⇒ x + y = 55

⇒ 13 + y = 55

⇒ y = 42.

Therefore,

⇒ The age of elder sister = 13 years.

⇒ The age of father = 42 years.

Hope it helps!