In the expression xy2 , the value of both variables x and y are decreased by 20%. By this, the value of the expression is decreased by :

Answer: Option B

Let X and Y denote the new values of x and y respectively.
Then, X = 80% of x = $$\frac{4x}{5}$$
Y = 80% of y = $$\frac{4y}{5}$$
$$\begin{array}{rl}& \therefore X{Y}^2=\frac{4x}{5}\times {\left(\frac{4y}{5}\right)}^2\\ & =\frac{4x}{5}\times \frac{16y^2}{5}\\ & =\frac{64}{125}x{y}^2\end{array}$$
Decrease in the value :
$$\begin{array}{rl}& =\left(x{y}^2-\frac{64}{125}x{y}^2\right)\\ & =\frac{61}{125}x{y}^2\end{array}$$
∴ Decrease %
$$\begin{array}{rl}& =\frac{61}{125}x{y}^2\\ & =\left(\frac{61x{y}^2}{125}\times \frac{1}{x{y}^2}\times 100\right)\%\\ & =48.8\%\end{array}$$