Question : 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 a speed of 12 km/hr completes one round in 8 minutes, then the area of the park is:
Option 1: 1,53,650 sq. metres
Option 2: 1,35,600 sq. metres
Option 3: 1,53,600 sq. metres
Option 4: 1,56,300 sq. metres
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Correct Answer: 1,53,600 sq. metres
Solution : Given: The ratio between the length and the breadth of a rectangular park is 3 : 2. Let length be $3x$, breadth be $2x$. A man cycling along the boundary of the park at a speed of 12 km/hr completes one round in 8 minutes. 1 hour = 60 minutes So, circumference of the park = $\frac{12}{60}×8$ = $1.6$ km = 1600 metres Therefore, $2×(3x+2x)=1600$ ⇒ $10x = 1600$ $\therefore x = 160$ So, Length = 3 × 160 = 320 metres Breadth = 2 × 160 = 480 metres Area of the park = 320 × 480 = 1,53,600 sq. metres Hence, the correct answer is 1,53,600 sq. metres.
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