Discussion

Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?

Answer: C

Use the ratio to write both sides with one unknown.

\[ 3k \times 2k = 3750 \quad\Longrightarrow\quad 6k^{2} = 3750 \quad\Longrightarrow\quad k^{2} = 625 \]

\[ k = 25 \quad\Longrightarrow\quad \text{sides} = 75 \text{ m and } 50 \text{ m} \]

\[ \text{perimeter} = 2(75 + 50) = 250 \text{ m} \]

\[ \text{cost} = 250 \times \text{Rs. } 0.50 = \text{Rs. } 125 \]

50 paise is half a rupee, so the cost is half the perimeter in rupees - treating the rate as Rs. 50 would inflate the answer a hundredfold.

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