An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 3 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?	Options:
A) 12:7 B) 15:11 C) 25:16 D) 30:23 E) 32:25
Let the length and width of one carpet be 3x and 2x.   Let the length and width of the other carpet be 3y and y.   2(3x + 2x) = 2(3y + y)   5x = 4y   (5/4) * x = y   The ratio of the areas of the carpet in both cases:   = 3x * 2x : 3y * y   = 6x^2 : 3y^2   = 6x^2 : 3*(25/16) * x^2   = 96 : 75   = 32 : 25   The answer is 32:25.
<result>E</result>
An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 3 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?