The ratio of the length to the breadth of a rectangular park is 3:2. A man cycles once along the boundary of the park at a speed of 12 km/hr and completes one full round in 8 minutes. Using this information, find the area of the park in square metres (sq m).

Introduction / Context:
This problem combines speed-time-distance with rectangle perimeter and ratio-based dimensions. Cycling along the boundary gives the perimeter because distance traveled in one round equals the total boundary length. Once the perimeter is known, the 3:2 ratio lets you express length and breadth in terms of a single variable and solve for both. Finally, multiply length and breadth to obtain the area. The question tests multi-step reasoning and correct unit conversion (km/hr to m/min).

Given Data / Assumptions:

• Length:Breadth = 3:2
• Speed = 12 km/hr
• Time for one round = 8 minutes
• Perimeter = distance traveled in one round

Concept / Approach:
Distance = Speed * Time. Convert 12 km/hr into metres per minute, multiply by 8 minutes to get perimeter. Let length = 3x and breadth = 2x. Then perimeter = 2*(3x + 2x) = 10x. Solve for x, then compute area = (3x)*(2x).

Step-by-Step Solution:
Convert speed: 12 km/hr = 12*1000 m / 60 min = 200 m/minDistance in 8 min = 200*8 = 1600 mSo perimeter P = 1600 mLet length = 3x and breadth = 2xPerimeter: 2*(3x + 2x) = 2*(5x) = 10x10x = 1600 => x = 160Length = 3x = 480 m, Breadth = 2x = 320 mArea = 480*320 = 153600 sq m

Verification / Alternative check:
Check perimeter: 2*(480+320) = 2*800 = 1600 m, matches the cycling distance. Area magnitude is reasonable for a park with sides 480 m and 320 m (both under 0.5 km). Everything is consistent.

Why Other Options Are Wrong:
13600 and 16300 are far too small and usually come from failing to convert km/hr to m/min. 143600 and 156300 typically appear from arithmetic slips in multiplying 480*320 or using an incorrect x due to wrong perimeter formula.

Common Pitfalls:
Not converting hours to minutes. Treating 8 minutes as 8 hours or 8 seconds. Using area formula when you actually need perimeter first. Using 3x+2x as area directly. Miscomputing 480*320.

Final Answer:
153600 sq m