2-D Mensuration Quants question

Q) The length and breadth of a rectangle are in the ratio 3 : 2 and their perimeter is 2000 metres. If the length is increased in the ratio 1 : 2 and the breadth is increased in the ratio 2 : 3, then find out the proportion of resulting rectangle area to the existing rectangle area.

7 : 8

4 : 5

5 : 2

3 : 1

9 : 8                      
Solution: Let us take the length of the rectangle as '3x' and breadth as '2x'.
Perimeter of the rectangle is 2 x (length + breadth) = 2000 metres i.e. 2 x (3x + 2x) = 2000
2  (5x) = 2000
10x = 2000
x = 2000/10 = 200
Therefore, the length = 3  200 = 600 metres
Breadth = 2  200 = 400 metres
Area of the existing rectangle = Length  Breadth
= 600  400
= 240000 sq. mts
If the length is increased in the ratio 1 : 2, then new length = 600/1  2 = 1200 metres
If the breadth is increased in the ratio 2 : 3, then new breadth = 400/2  3 = 600 metres
Area of resulting rectangle = 1200  600 = 720000 sq. mts
Therefore, the proportion of resulting rectangle area to the existing rectangle area is 720000 : 240000
i.e. 3 : 1