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 4 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?  Choices.
A) 5 : 8	B) 3 : 2	C) 6 : 1	D) 8 : 7	E) 5 : 6

Rationale: let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 4 y and y . 2 ( 3 x + 2 x ) = 2 ( 4 y + y ) 5 x = 5 y x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 4 y * y = 6 x ^ 2 : 4 y ^ 2 = 6 x ^ 2 : 4 x ^ 2 = 6 : 4 = 3 : 2 the answer is b .
Answer: B