Question

A property dealer bought a rectangular piece of land at 1000/sq. ft. The length of the plot is less than twice its breadth. Due to its size, there were no buyers for the full plot. Hence he decided to sell it in smaller sized pieces as given below. The largest square from one end was sold at 1200/sq. ft. From the remaining rectangle the largest square was sold at 1150/sq. ft. Due to crash in the property prices, the dealer found it difficult to make profit from the sale of the remaining part of

Accepted Answer

B. Let original dimensions be length $l$ and breadth $b$, with $b < l < 2b$. 1) Cut largest square $b 	imes b$, area $b^2$, leaving rectangle $(l-b) 	imes b$. 2) Cut largest square from remaining: side $(l-b)$, area $(l-b)^2$. 3) Remaining rectangle GHCF has length $l-b$ and breadth $b - (l-b) = 2b - l$. Perimeter GHCF = $2[(l-b) + (2b-l)] = 2b$. Perimeter original = $2(l+b)$. Given $\frac{2b}{2(l+b)} = \frac{3}{8} \implies 8b = 3l + 3b \implies 5b = 3l \implies l = 5, b = 3$. Total area = $15$ sq ft. Total cost @ 1000 = 15,000. Target SP (10% profit) = 16,500. First square SP ($3^2 	imes 1200$) = $9 	imes 1200 = 10,800$. Second square SP ($2^2 	imes 1150$) = $4 	imes 1150 = 4,600$. Remaining area = $15 - 9 - 4 = 2$ sq ft. Let selling price per sq ft be $x$. $10,800 + 4,600 + 2x = 16,500 \implies 15,400 + 2x = 16,500 \implies 2x = 1100 \implies x = 550$/sq. ft.

Property Dealer Rectangular Land Plot

Explanation

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