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CAT-2003-Previous Years Paper

Question
18 out of 50
 

Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from square cloth piece of side a in the following steps: the original square of side a is divided into smaller squares, not necessarily of the same size, then a circle of maximum possible area is from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes: The ratio of the total area of scrap cloth generated in the former to that in the latter, is



A 1:1
B

C
D

Ans. A

Consider a square of side x.

Therefore, its area = x2

Therefore, the area of the largest circle = Π

Which can be cut from the square =

Therefore, the area scrapped =

= Constant

As this ratio is constant whether we cut a circle from the smaller square or the larger square, the scrapped area will be a fixed percentage of the square. Therefore, in this problem, as the two squares are of the same size, the ratio will be 1:1

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