Question

Rakhi is 26years younger than her mother. In 9years, her mother will be twice as old as Rakhi. how old of each

Answer 1

Answer :

Rakhi is 17 years old

Her mother is 43 years old.

Step-by-step explanation :

⇒ Rakhi is 26years younger than her mother.

    Let the present age of her mother be "x"

      Then present age of Rakhi = x - 26

⇒ In 9years, her mother will be twice as old as Rakhi

     After 9 years,

        age of her mother = (x + 9)

        age of Rakhi = (x - 26 + 9)

                              = (x - 17)

[ her mother will be twice as old as Rakhi ]

     x + 9 = 2(x - 17)

     x + 9 = 2x - 34

     2x - x = 34 + 9

         x = 43

Present age of her mother = 43

Present age of Rakhi = 43 - 26 = 17

     

Answer 2

The present age of Rakhi and her mother :

• The present age of Rakhi = 17 years.
• The present age of her mother = 43 years.

Given :

• The age of Rakhi is 26 years younger than her mother.
• After 9 years, the age of her mother will be twice as old as Rakhi.

To Find :

• The present age of Rakhi and her mother.

Solution :

Let,

The age of Rakhi be x.

The age of her mother be x + 26 because according to the question, Rakhi is 26 years younger than her mother. That means, her mother is 26 years older than Rakhi.

After 9 years,

The age of Rakhi = x + 9.

The age of her mother = x + 26 + 9 = x + 35.

According to the condition,

After 9 years, the age of her mother will be twice as old as the age of Rakhi.

That means,

$: \implies \bf x + 35 = 2(x + 9) \\ \\ \\ : \implies \bf x + 35 = 2x + 18 \\ \\ \\ : \implies \bf 35 - 18 = 2x - x \\ \\ \\ : \implies \bf 17 = x \\ \\ \\ \: \: \bf \therefore \: \: x = 17 \: years$

So, the present age of Rakhi and her mother :

★ Rakhi's age = x = 17 years.

★ Her mother's age = x + 26 = 17 + 26 = 43 years.

Hence,

The present age of Rakhi and her mother is 17 years and 43 years.