If $z=\frac{x^{2}}{y}$ and $x, y$ are both increased in value by 10\%, find the percentage change in the value of $z$. (M.B.A., 2007)
Answer
Answer (as printed):
Explanation
Let $X, Y$ and $Z$ represent the changed values of $x, y$ and $z$ respectively. Then, $X=110\%$ of $x=\frac{11x}{10}$; $Y=110\%$ of $y=\frac{11y}{10}$. $Z=\frac{X^{2}}{Y}=\frac{\left(\frac{11x}{10}\right)^{2}}{\left(\frac{11y}{10}\right)}=\frac{11}{10}\cdot\frac{x^{2}}{y}=\frac{11}{10}z$. Increase in the value of $z=\left(\frac{11z}{10}-z\right)=\frac{z}{10}$. Increase $\%=\left(\frac{z}{10}\times\frac{1}{z}\times 100\right)\%=10\%$.
Explanation as extracted from the printed page; notation may be imperfect.