Seven years ago,raghav's age was five …

Let the present age of Namita = x years.

Seven Years ago The Age of Namita = (x - 7) years.

Then the age of Raghav = 5(x - 7)^2

Therefore Raghav's present age = 5(x - 7)^2 + 7

= 5(x^2 + 49 - 14x) + 7

= 5x^2 + 245 - 70x + 7

= 5x^2 - 70x + 252. --------- (1)

Three Years Hence:

The age of Namita = (x + 3) years.

The age of Raghav = (5x^2 - 70x + 252) + 3

= 5x^2 - 70x + 255 years.

Given that Namita's age will be 2/5 times of Raghav's age.

x + 3 = 2/5(5x^2 - 70x + 255)

5x + 15 = 10x^2 - 140x + 510

10x^2 - 140x + 510 - 15 = 5x + 15

10x^2 - 140x + 495 = 5x + 15

10x^2 - 145x + 495 = 0

2x^2 - 29x + 99 = 0

2x^2 - 18x - 11x + 99 = 0

2x(x - 9) - 11(x - 9) = 0

(2x - 11)(x - 9) = 0

2x = 11 (or) x = 9

x = 11/2 (or) x = 9.

Since age cannot be a fraction, So x = 9.

Substitute x = 9 in (1), we get

5x^2 - 70x + 252

5(9)^2 - 70(9) + 252

405 - 630 + 252

657 - 630

= 27 years.

Therefore the present age of Namita = 9 years.

Therefore the present age of Raghav = 27 years.

The difference between their ages = 18 years.