Answer : Option D

Explanation :

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Solution 1
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Let original length = 100 and original breadth = 100
Then original area = 100 × 100 = 10000

$MF#%\begin{align}&\text{Length of the rectangle is halved}\\
&\Rightarrow\text{New length = }\dfrac{\text{Original length}}{2} = \dfrac{100}{2} = 50\\\\\\
&\text{breadth is tripled}\\
&\Rightarrow \text{New breadth= Original breadth}\times 3 = 100 \times 3 = 300\\\\
\end{align} $MF#%

$MF#%\text{Percentage of Increase in area = }\dfrac{\text{Increase in Area}}{\text{Original Area}} \times 100 = \dfrac{5000}{10000} \times 100 = 50\% $MF#%

$MF#%\begin{align}
&\text{Length of the rectangle is halved}\\
&\Rightarrow \text{New length = }\dfrac{\text{Original length}}{2} = \dfrac{l}{2}\\\\\\
&\text{breadth is tripled}\\
&\Rightarrow \text{New breadth = Original breadth}\times 3 = 3b \\\\
&\text{New area = }\dfrac{l}{2}\times 3b = \dfrac{3lb}{2}\\\\
&\text{Increase in area = New Area - Original Area = } \dfrac{3lb}{2} - lb = \dfrac{lb}{2}\\\\
&\text{Percentage of Increase in area = }\dfrac{\text{Increase in Area}}{\text{Original Area}} \times 100 \\
&= \dfrac{\left(\dfrac{lb}{2}\right)}{lb} \times 100 = \dfrac{lb \times 100}{2lb} = 50\% \end{align} $MF#%