If the length of a rectangle is increased by \(66 \frac{2}{3} \%\), then by what percent should the width of the rectangle be decreased in order to maintain the same area ?  

Shortcut Trick 

⇒ % decrease in width = (2/5) × 100 = 40%

∴ The required value is 40%.

Alternate Method 
Given:

Increased length = Original length + (2/3) of original length

Concept used:

New area = Original area

% Change = [(Final value - Initial value)/Initial value ] × 100

Calculation:

Let the length and width of the rectangle be L and W respectively.

Original area = Length × Width = L × W

New length = Original length + (2/3) of original length

New length = L + (2/3)L = (5/3)L

New area = New length × New width

New area = (5/3)L × New width

According to the question, New area = Original area

(5/3)L × New width = L × W

New width = (3/5)W

Now, the percent decrease in width

⇒ [(W - 3W/5) / W] × 100 

Percent decrease in width = (2/5) × 100 = 40%

∴ The required value is 40%.