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

A. 25% increase

B. 50% increase

C. 50% decrease

D. 75% decrease

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}

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