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 :

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 : Correct Answer 48.8%

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 = $$\frac{4y}{5}$$
$$\eqalign{ & \therefore X{Y^2} = \frac{{4x}}{5} \times {\left( {\frac{{4y}}{5}} \right)^2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{4x}}{5} \times \frac{{16{y^2}}}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{64}}{{125}}x{y^2} \cr} $$
Decrease in the value :
$$\eqalign{ & = \left( {x{y^2} - \frac{{64}}{{125}}x{y^2}} \right) \cr & = \frac{{61}}{{125}}x{y^2} \cr} $$
∴ Decrease %
$$\eqalign{ & = \frac{{61}}{{125}}x{y^2} \cr & = \left( {\frac{{61x{y^2}}}{{125}} \times \frac{1}{{x{y^2}}} \times 100} \right)\% \cr & = 48.8\% \cr} $$