If the length of a rectangle is increased by 40%, and the breadth is decreased by 20%,then the area of the rectangle increases by x%. Then the value of x is:

Area of the rectangle = length $$\times$$ breadth

now,

Length = 140% of length = 1.4length

breadth = 80% of breadth = 0.8breadth

Area of rectangle = 1.4length $$\times$$ 0.8breadth = 1.12 length $$\times$$ breadth

Increment in area of rectangle = 1.12 length $$\times$$ breadth - length $$\times$$ breadth = 0.12 length $$\times$$ breadth

Percentage increment in area of rectangle = $$\frac{ 0.12 length $$\times$$ breadth}{length $$\times$$ breadth} \times 100

x% = 12%