Question: A property dealer bought a rectangular piece of land at Rs. 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 Rs. 1200/sq. ft. From the remaining rectangle the largest square was sold at Rs. 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 the land. If the ratio of the perimeter of the remaining land to the perimeter of the original land is 3 : 8, at what price (in Rs.) the remaining part of the land is to be sold such that the dealer makes an overall profit of 10%?
Explanation:
Consider the following diagram.
Here, a is the length of the plot and b is the height of the plot.
Hence, from the diagram, perimeter of the remaining portion is;
2 × (2b – a + a – b) = 2b
Perimeter of the original land = 2(a + b)
Hence, we have, 2b : 2(a + b) = 3 : 8
Hence, b : a = 3 : 5
Now, without loss of generality we can assume that a = 5 and b = 3
Hence, area of the land = 15 square unit.
Hence, cost of the land = 1000 × 15
Now, selling price of small and big squares are, 9 × 1200 and 4 × 1150 respectively.
Let he sells the remaining land at Rs. x/sq. ft.
Hence, we have,
9 × 1200 + 4 × 1150 + x × 2 = 1100 × 15
Hence, x = 550
Hence, option (b).