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 ​

Answer 1

Answer:

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

Step-by-step explanation:

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  

Answer 2

Answer:

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Step-by-step explanation:

so let the present age of swapna's mother be x years and that of swapna be y years

according to the first condition

x-4=3(y-4)

ie x-4=3y-12

so x=-8+3y

ie x=3y-8 (1)

according to second condition

x+6=2(y+6)

x+6=2y+12

ie x=2y+6 (2)

equating both equations we get

2y+6=3y-8

ie y=14

substituting value of y in any of two equations

we get

x=34

hence present age of swapna's mother is 34 years and that of swapna is 14 years