Question

In the expression $x{y}^2$ the values of both variables $x$ and $y$ are decreased by $20\%$. By this the value of the expression will be decreased by

• A. $40\%$
• B. $80\%$
• C. $48.8\%$
• D. $51.2\%$

Answer 1

The correct option is C $48.8\%$

New value of $x$ $=\frac{80}{100}x=0.8x$
New value of $y^2=\frac{80}{100}y\times \frac{80}{100}y=0.64y^2$
$\therefore$ New value of expression $=0.8x\times 0.64y^2=0.512x{y}^2$
$\therefore$ $\%$ reduction in the value $=\frac{xy-0.512x{y}^2}{x{y}^2}\times 100\%$
$=(0.488\times 100)\%$

$=48.8\%$