The length of a rectangle is increased by 60%. By what percent would the width be decreased so as to maintain the same area?
$
  {\text{A}}{\text{. }}37\dfrac{1}{2}\% \\
  {\text{B}}{\text{. }}60\% \\
  {\text{C}}{\text{. }}75\% \\
  {\text{D}}{\text{. 120% }} \\
 $

Hint: Here we go through by first finding the original area by letting the original length be 100 and also take the breadth be 100. Then increase the length of the rectangle as suggested in the question and assume that the breadth is decreasing at the rate of x and then find the new area which is equal to the original area to find the value of x.

Complete step-by-step answer:
Let length of rectangle =100 m
And the breadth of rectangle =100 m
As we know the area of the rectangle is (Length$ \times $Breadth).
Therefor the original area $100 \times 100 = 10000{m^2}$
Here in the question it is given that the length of the rectangle is increased by 60%.
First we find 60% of the length then add it to the original length to find out the new length i.e. 100+60% of 100$ = 100 + \dfrac{{60}}{{100}} \times 100 = 160m$
And we assume that the length is decreasing at the x%
First we find x% of the breadth then subtract it to the original breadth to find out the new breadth i.e. 100+x% of 100$ = 100 - \dfrac{x}{{100}} \times 100 = (100 - x)m$
Therefore the new area$ = 160 \times (100 - x)$
According to the question the area should be same i.e.
$
   \Rightarrow 160 \times (100 - x) = 10000 \\
   \Rightarrow (100 - x) = \dfrac{{10000}}{{160}} \\
   \Rightarrow x = 100 - \dfrac{{125}}{2} \\
  \therefore x = 37.5\% \\
 $
Therefore percent decrease in breadth is 37.5%.
Hence option A is the correct answer.

Note: Whenever we face such type of question the key concept for facing the problem is whenever in the question data is not given only given that the changes of percentage then let the original data as 100 for easy solving of percentage. And then assume the result which we have to find as a variable then apply the condition of question to find out that variable.