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Question 58

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

Solution

Let length and breadth of the rectangular park be 3x and 2x

Distance covered by the man cycling around the park (in meters) is given by,

$$12 \times \frac{5}{18} \times 8 \times 60 = 1600$$

Perimeter of the rectangular park is equal to 1600

$$\therefore$$ 2(3x + 2x) = 1600

5x = 800 (or) x = 160

Area of the park = $$\times$$ 6x$$^{2}$$

= 6(160 x 160)

= 153600 sq.m

Hence, option B is the correct answer.

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