Let present age of the son be x years
∴ Present age of the father = x² years
one year ago,
Age of the son = (x – 1) years
and Age of the father = (x² – 1) years
According to the given condition,
x² – 1 = 8(x – 1)
⇒ x² – 1 – 8x + 8 = 0
x² – 8x + 7 = 0
⇒ (x – 1) (x– 7) = 0
⇒ x – 1 = 0,  x – 7 = 0
i.e., x = 1,  x = 7
When x = 1, age of son = age of father, which is impossible
∴ x = 1 is rejected.
∴ x = 7
Thus present age of son = 7 years
and present age of father = 49 years.

Let present age of son = x years
Two years ago, Age of son = (x – 2) years
Age of man = 3(x – 2)²
∴ Man’s present age = 3(x – 2)² + 2
= 3(x² – 4x + 4) + 2
= 3x² – 12x + 14
Age of man = 3(x – 2)²
∴ Man’s present age = 3(x – 2)² + 2
= 3(x² – 4x + 4) + 2
= 3x² – 12x + 14
After 3 year
The age of son  = (x + 3) years
Age of man  
According to given condition,
                

Since, 
∴    The present age of man
                             

Let the present age of father be x years. Then,
Son’s present age = (45 – x) years
Five years ago,
Age of Father = (x – 5) years
and Age of Son = (45 – x – 5) years = (40 – x) years
According to given condition,
(x – 5) (40 – x) = 124
⇒ 40x – x² – 200 + 5x = 124
⇒ x² – 45x + 324 = 0
⇒ x² – 36x – 9x + 324 = 0
⇒ x (x – 36) – 9 (x – 36) – 0
⇒ (x - 9) (x - 36) = 0
⇒x = 9 or x = 36
When x = 36, we have
Father’s present age = 36 years
Son’s present age = 9 years
When x = 9, we have
Father’s present age = 9 years
Son’s present age = 36 years
Clearly, this is not possible
Hence, Father’s present age = 36 years and Son’s present age = 9 years.

Seven years ago, let Swati’s age be x years.
Then, seven years ago Varun’s age was 5x² years.
∴ Swati’s present age = (x + 7) years
Varun’s present age = (5x² + 7) years
Three years hence,
Swati’s age = (x + 7 + 3) years
= (x + 10) years
and Varun’s age = (5x² + 7 + 3) years
= (5x² + 10) years
According to given condition,
∴               

Hence, Swati's present age = (2 + 7) years  = 9 years
  Varun's present age =