CAT Quantitative Ability Questions | CAT Mensuration questions
CAT/2003
Question . 44
Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps : the original square of side a is divided into n smaller squares, not necessarily of the same size ; then a circle of maximum possible area is cut 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
Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Mensuration question
(a) First Process : Consider a square of side a, which is divided into n squares of different sides. In each square there is a circle of maximum area cut out. The remaining area of square is scrap. For any square say side be b
The ratio remains same for all the squares combined. Second Process : The above ratio is
Hence, the required ratio = 1 : 1