Question

If the length of a rectangle is increased by one-third and its width is decreased by one-third, then find the percentage decrease in its area.

• A. $\frac{8}{9}$ %
• B. $\frac{1}{9}$ %
• C. $11\frac{1}{9}$ %
• D. $\frac{2}{3}$ %

Answer 1

The correct option is C $11\frac{1}{9}$ %

Let the original length and breadth of the rectangle be $l$ and $b$ units. Then, original area $=l\times b$ sq units

New breadth $=l+\frac{1}{3}l=\frac{4}{3}l$

New breadth $=b-\frac{1}{3}b=\frac{2}{3}b$

$\therefore$ New area $=\frac{4}{3}l\times \frac{2}{3}b=\frac{8}{9}lb$ sq units

$\therefore$ Decrease in area $=(\frac{lb-\frac{8}{9}lb}{lb}\times 100)\%=\frac{\frac{1}{9}lb}{lb}\times 100\%=\frac{100}{9}\%=11\frac{1}{9}\%$