The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

Let original length = x and original breadth = y.

Original area = xy. 

New length = x/2 and New breadth=3y 

New area =  $\frac{3}{2}xy$ 

Therefore,  Increase in area = New area-original area =  $\frac{3}{2}xy-xy=\frac{1}{2}xy$ 

Therefore,  Increase % =  $\frac{increase in area }{original area}*100=\frac{\frac{1}{2}}{x}*100=50$ %