Question

4 years ago, Swapana mother was 3 times as old as swapana.After 6 years she will be twice as old as swapana.present age of Swapana mother is​

Answer 1

Step-by-step explanation:

4 years ago,

Let,

• The age of Swapana = x
• The age of Swapana's mother = 3x

★ Present age,

• Present age of Swapana = x + 4
• Present age of Swapana's mother = 3x + 4

After 6 years,

• Age of Swapana = x + 4 + 6 = x + 10
• Age of Swapana's mother = 3x + 4 + 6 = 3x + 10

Also,

Swapana's mother will be twice as old as Swapana

★ According to the Question :

⇒ 2 (x + 10) = 3x + 10

⇒ 2x + 20 = 3x + 10

⇒ 20 - 10 = 3x - 2x

⇒ 10 = x

___________________________

• Present age of Swapana = x + 4

⇒ x + 4

⇒ 10 + 4

⇒ 14

Present age of Swapana = 14 years

___________________________

• Present age of Swapana's mother = 3x + 4

⇒ 3x + 4

⇒ 3 (10) + 4

⇒ 30 + 4

⇒ 34

Present age of Swapana's mother = 34 years

Therefore, present age of Swapana's mother is 34 years.

Answer 2

Given :-

4 years ago, Swapana's mother was 3 times as old as Swapana. After 6 years she will be twice as old as Swapna.

To Find :-

The Present age of Swapana's mother

Solution :-

Let the age of Swapana be x and her mother age be y

Four years ago

Age of Swapana = x - 4

Age of mother = y - 4

According to the question

Mother's age = 3(Swapana Age)

y - 4 = 3(x -  4)

y - 4 = 3x - 12

y - 3x = 4 + (-12)

y - 3x = 4 - 12

y - 3x = -8 (..i)

After 6 years

Age of Swapana = x + 6

Age of mother = y + 6

Mother's age = 2(Swapana Age)

y + 6 = 2(x + 6)

y + 6 = 2x + 12

y - 2x = 12 - 6

y - 2x = 6 (..ii)

On subtracting

y - 3x - (y - 2x) = -8 - 6

y - 3x - y + 2x = -14

-3x + 2x = -14

-x = -14

x = 14

Using Eq 2

y - 2(14) = 6

y - 28 = 6

y = 28 + 6

y = 34

Hence

Age of her mother is 34 years.