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Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. He dug a square shaped pond inside the farm whose side is 1/3 of the breadth. The area of the farm is 20 times the area of ...

Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is \(\frac{1}{3}\) of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond

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Answer: Farm: breadth 45 m, length 100 m; pond side 15 m

Let the breadth be \(x\) m. Length \(= 2x + 10\); side of pond \(= \frac{x}{3}\).

\[x(2x + 10) = 20\left(\frac{x}{3}\right)^2\]\[2x^2 + 10x = \frac{20x^2}{9}\]\[18x^2 + 90x = 20x^2\]\[2x^2 - 90x = 0\]\[2x(x - 45) = 0\]

\(x = 45\) (breadth cannot be 0). Length \(= 100\) m, pond side \(= 15\) m. Check: \(4500 = 20 \times 225\).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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