The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

15360

153600

30720

307200

Explanation:

Perimeter = Distance covered in 8 min. =$ \left(\dfrac{12000}{60} \times 8\right) $m = 1600 m.

Let length = 3$x$ metres and breadth = 2$x$ metres.

Then, 2$\left(3x + 2x\right) = 1600 $ or $x$ = 160.

$\therefore$ Length = 480 m and Breadth = 320 m.

$\therefore Area = (480 \times 320)$ m² = 153600 m².