The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. Find the length of the rectangle?

Let the breadth of the given rectangle be x then length is 2x.
thus area of the given rect is  2 x 2

after dec 5cm from length and inc 5cm breadth , new lenght becomes 2x-5 and breadth is x+5.thus new area =(2x-5)(x+5)= 2 x 2 + 5 x - 25

since new area is 75 units greater than original area thus
2 x 2 + 75 = 2 x + 5 x - 25
5x=75+25
5x=100
therefore x=20
hence length of the rectangle is 40 cm.