If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be :

Solution (By Examveda Team)

Let the original length and breadth of the rectangle be $$l$$ and b respectively.
Then,
Original area = $$lb$$
New length :
$$ = 110\% {\text{ of }}l = \frac{{11}}{{10}}l$$
New breadth :
$$ = 90\% {\text{ of }}b = \frac{{9}}{{10}}b$$
New area :
$$\eqalign{ & = \left( {\frac{{11}}{{10}}l \times \frac{{9}}{{10}}}b \right) \cr & = \frac{{99}}{{100}}lb \cr} $$
Decrease in area :
$$\eqalign{ & = \left( {lb - \frac{{99}}{{100}}}lb \right) \cr & = \frac{{lb}}{{100}} \cr} $$
∴ Decrease % :
$$\eqalign{ & = \left( {\frac{{lb}}{{100}} \times \frac{1}{{1b}} \times 100} \right)\% \cr & = 1\% \cr} $$