On increasing the length and breadth of a rectangle by 1 m, the area increases by 21 m².  If its length is increased by 1 m but breadth decreases by 1m, area decreases by 5 m².  the perimeter of the rectangle is:

40 m

Let Length of rectangle be x metre and breadth by y metre 

                area = xy m²

Case I    

(x+1) (y+1) - xy = 21

⇒ xy + x + y + 1 - xy = 21

⇒ x + y = 20

Case II

xy - (x+1) (y-1) = 5

⇒ xy - xy + x - y = 4

⇒ x - y = 4

On solving, x = 12, y = 8

∴ perimeter = 2(12+8) = 40 m