Discussion

If the length is increased by 25%, by what percent the width of a rectangle should be decreased so as to keep the area same.

Answer: B

The area must stay fixed, so the two factors have to multiply to 1.

\[ 1.25 \times (1 - d) = 1 \quad\Longrightarrow\quad 1 - d = \frac{1}{1.25} = 0.8 \]

\[ d = 0.2 = 20\% \]

A 25% rise is undone by a 20%, not a 25%, fall, because the reduction applies to the larger figure. The general rule is

\[ d = \frac{x}{100 + x} \times 100 = \frac{25}{125} \times 100 = 20\% \]

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