CTET 2 Math and Science 2011 Paper

Let side of a square be 'a' unit. Since one side is decreased by 20%
∴ one side $=\mathit{a}-\frac{\mathit{a}\times 20}{100}=\frac{4\mathit{a}}{5}$
and another adjacent side is decreased by 40%
∴Another adjacent side $=\mathit{a}-\mathit{a}\times \frac{40}{100}=\frac{3\mathit{a}}{5}$
∴ New area of square $=\frac{4\mathit{a}}{5}\times \frac{3\mathit{a}}{5}=\frac{12{\mathit{a}}^2}{25}$
Required $\%={\mathit{a}}^2-\frac{12{\mathit{a}}^2}{25}=\frac{13{\mathit{a}}^2}{25}$
$=\frac{13\times 100}{25}\%=52\%$