The length of a rectangle is increased by $ 10\%$ and the width is decreased by $ 10\%$. What percent of the old area is the new area?


$ \textbf{(A)}\  90  \qquad
\textbf{(B)}\   99  \qquad
\textbf{(C)}\   100  \qquad
\textbf{(D)}\   101  \qquad
\textbf{(E)}\   110$
1. Let the original length of the rectangle be \( l \) and the original width be \( w \). The original area \( A \) of the rectangle is given by:
   \[
   A = l \times w
   \]

2. The length is increased by \( 10\% \). Therefore, the new length \( l' \) is:
   \[
   l' = l \times 1.1
   \]

3. The width is decreased by \( 10\% \). Therefore, the new width \( w' \) is:
   \[
   w' = w \times 0.9
   \]

4. The new area \( A' \) of the rectangle with the new dimensions is:
   \[
   A' = l' \times w' = (l \times 1.1) \times (w \times 0.9) = l \times w \times 1.1 \times 0.9
   \]

5. Simplify the expression for the new area:
   \[
   A' = l \times w \times 0.99 = 0.99 \times A
   \]

6. The new area is \( 99\% \) of the original area.

The final answer is \( \boxed{99} \)