The length of a rectangle is increased by $$16\frac{2}{3} \%$$. By what approximate percentage should its breadth be decreased so that the area of the rectangle remains unchanged?

Let's assume the initial length and breadth of a rectangle is 42y and 42z respectively.

 initial area of a rectangle = $$42y\times\ 42z$$ = 1764yz

The length of a rectangle is increased by $$16\frac{2}{3} \%$$.

length of a rectangle after increase = 42y of $$(100+16\frac{2}{3}) \%$$

= $$42y\ of\ (100+\frac{50}{3})\%$$

= $$42y\ of\ \frac{350}{3}\%$$

= $$42y\times\frac{350}{300}$$

The approximate percentage decreased in the breadth of the rectangle = $$\frac{initial\ breadth\ -\ new\ breadth}{initial\ breadth}\times\ 100$$

= $$\frac{42z-36z}{42z}\times\ 100$$

= $$\frac{6z}{42z}\times\ 100$$

= $$\frac{1}{7}\times\ 100$$

= 14.29% approx.