The length of a rectangle is decreased by r%, and the breadth is increased by (r + 5)%. Find r, if the area of the rectangle is unaltered :

Let original length = x and original breadth = y
Then,
Original area = xy
New area :
$$\eqalign{ & = \left[ {\frac{{\left( {100 - r} \right)}}{{100}} \times x} \right]\left[ {\frac{{\left( {105 + r} \right)}}{{100}} \times y} \right] \cr & = \left[ {\left( {\frac{{10500 - 5r - {r^2}}}{{10000}}} \right)xy} \right] \cr & \therefore \left( {\frac{{10500 - 5r - {r^2}}}{{10000}}} \right)xy = xy \cr & \Rightarrow {r^2} + 5r - 500 = 0 \cr & \Rightarrow \left( {r + 25} \right)\left( {r - 20} \right) = 0 \cr & \Rightarrow r = 20 \cr} $$