Question

If the base of a rectangle is increased by $10$% and the area is unchanged then the altitude is decreased by

• A. $9$%
• B. $10$%
• C. $11$%
• D. $11\frac{1}{9}$%
• E. $9\frac{1}{11}$%

Answer 1

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

$bh=\left(\frac{11}{10}b\right)\left(xh\right)\therefore x=\frac{10}{11}$ and $h$ is reduced by $\frac{1}{11}$ or $9\frac{1}{11}$%; or
$bh=(b+\frac{1}{10}b)(h-\frac{r}{100}h)=bh+\frac{1}{10}bh-\frac{r}{100}bh-\frac{r}{1000}bh$.
$\therefore \frac{1}{10}-\frac{r}{100}-\frac{r}{1000}=0$ and $r=9\frac{1}{11}$%.