Question

Four years ago, Shivani was thrice as old as Anjana . Eight years later, Shivani will be twice as old as Anjana . What are their present ages?​

Answer 1

Answer:

Present age of Shivani = 40 years

Present age of Anjana = 16 years

Step-by-step explanation:

Let the present age of Shivani = x years

Let the present age of Anjana = y years

Four years ago , Shivani was thrice as old as Anjana.

Four years ago , Shivani's age = ( x - 4 ) years

Four years ago , Anjana's age = ( y - 4 ) years

x - 4 = 3( y - 4 )

x - 4 = 3y - 12

x - 3y - 4 + 12 = 0

x - 3y + 8 = 0 .....(1)

Eight years later , Shivani will be twice as old as Anjana.

Eight years later , Shivani's age = ( x + 8 ) years

Eight years later , Anjana's age = ( y + 8 ) years

x + 8 = 2( y + 8 )

x + 8 = 2y + 16

x - 2y + 8 - 16 = 0

x - 2y - 8 = 0 .......(2)

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

x - 3y + 8 - ( x - 2y - 8 ) = 0

x - 3y + 8 - x + 2y + 8 = 0

- y + 16 =0

y = 16

Putting the value of y = 16 in equation (1)

x - 3y + 8 = 0

x - 3(16) + 8 = 0

x - 48 + 8 = 0

x - 40 = 0

x = 40

Present age of Shivani = 40 years

Present age of Anjana = 16 years