In the given figure, the area of the unshaded region is 35% of the area of the shaded field.  What is the value of x?

10

Shaded     :       Unshaded      =     Complete (rectangle)

  100         :            35             =        135

Here,

Area of Shaded part ⇒ 100R = 80 × 50 = 4000

⇒ 1R = 40

Therefore,

Area of complete rectangle ⇒ 135R = 135 × 40 = 5400

⇒ (80 + x) (50 + x) = 5400

⇒ x² + 130x + 4000 = 5400

⇒ x (x+ 130) = 5400 - 4000

⇒ x (x+ 130) = 1400

Check from the option: x = 10 satisfy the equation.

Therefore, value of x = 10.