The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

125% increase
250% increase
350% decrease
475% decrease

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let original length = x and \\ Original breadth = y \\ Original area = x y \\ New length = \frac{x}{2} \\ New breadth = 3 y \\ New area = (\frac{x}{2} \times 3 y) = \frac{3}{2} x y \\ ∴ Increase % = (\frac{1}{2} x y \times \frac{1}{x y} \times 100) \\ = 50 % \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{original}}\,{\text{length}} = x\,{\text{and}}\, \cr & {\text{Original}}\,{\text{breadth}} = y \cr & {\text{Original}}\,{\text{area}} = xy \cr & {\text{New}}\,{\text{length}} = \frac{x}{2} \cr & {\text{New}}\,{\text{breadth}} = 3y \cr & {\text{New}}\,{\text{area}} = \left( {\frac{x}{2} \times 3y} \right) = \frac{3}{2}xy \cr & \therefore {\text{Increase}}\,\% = \left( {\frac{1}{2}xy \times \frac{1}{{xy}} \times 100} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 50\% \cr}$