Question

4 years ago, swapna's mother was three times as old as swapna . after 6 years she will be twice as old as swapna . present age of swapna mother
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Answer 1

Given :- 4 years ago, swapna's mother was three times as old as swapna . after 6 years she will be twice as old as swapna . present age of swapna mother ?

Solution :-

4 years ago :-

• Mother : Swapna = 3 : 1

After 6 years :-

• Mother : Swapna = 2 : 1

So,

→ (3 : 1)

→ (2 : 1)

this ratio can be written as ,

→ (3 : 1)

→ 2(2 : 1) = 4 : 2

therefore,

→ (4 - 3) = (2 - 1) = 1 .

hence,

→ 1 is equal to gap between years = (4 + 6) = 10 years.

then,

→ 3 is equal to = 3 * 10 = 30 years. = Mother's age 4 years ago.

∴

→ Mother Present age = 30 + 4 = 34 years. (Ans.)

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Answer 2

Given : 4 years ago, Swapna's mother was three times as old as Swapna . After 6 years she will be twice as old as Swapna.  

 

To find : Present age of Swapna mother.

 

Solution :

Let present age of Swapna’s mother = x & present age of Swapna = y

4 years ago:

Swapna’s mother age = (x - 4) yr

Swapna age = (y - 4) yr

A.T.Q:

⇒(x – 4) = 3(y – 4)

⇒(x – 4) = 3y – 12

⇒ x – 3y = - 12 + 4

⇒x - 3y = - 8 ---------- (1)

After 6 years

Swapna’s mother age = (x + 6) yr

Swapna age = (y + 6) yr

A.T.Q

⇒(x + 6) = 2(y + 6)

⇒x + 6 = 2y + 12

⇒x – 2y = 12 - 6  

⇒x – 2y = 6 ----------- (2)

Subtracting equation (1) from equation (2), we get  :

⇒(x – 2y) - (x - 3y) = 6 - (- 8)

⇒x – 2y - x + 3y = 6 + 8

⇒ - 2y + 3y = 14

⇒ y  =  14 ----------- (3)

Putting this value of y in equation (1), we get  :

x - 3y = - 8

x - 3(14) = - 8

x – 42 = - 8

x = - 8 + 42

x = 34 years  

Hence, the present age of Swapna’s mother is 34 years.

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