Question : The length and breadth of a rectangular piece of land are in a ratio of 5 : 3. The owner spent Rs. 6,000 to surround it from all sides at Rs. 7.50 per metre. The difference between its length and breadth is:
Option 1: 50 metres
Option 2: 100 metres
Option 3: 150 metres
Option 4: 250 metres
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Correct Answer: 100 metres
Solution :
Let the length of the rectangle as $5x$ and the breadth as $3x$.
The perimeter of a rectangle = $2 \times (\text{length} + \text{breadth})$
The perimeter of this rectangle = $2 \times (5x + 3x) = 16x$
The cost to surrounding the rectangle is Rs. $6,000$, and the cost per metre is Rs. $7.50$.
The total length of the fence in metres = $\frac{6000}{7.5} = 800$ metres
Now, the perimeter of this rectangle is equal to the total length of the fence in metres.
$16x = 800$
⇒ $x = 50$
The difference between the length and breadth = $5x - 3x = 2x = 2 \times 50 = 100$ metres.
Hence, the correct answer is 100 metres.
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