Question : A number is increased by $x$% to get back to the original number. It is to be reduced by:

Option 1: $x$%

Option 2: $\frac{100x}{100+x}$%

Option 3: $\frac{10x}{100+x}$%

Option 4: $\frac{x}{100+x}$%

Question : If the diameter of a sphere is reduced to its half, then the volume would be:

Option 1: increased by $\frac{1}{4}$ of the former volume

Option 2: reduced by $\frac{1}{4}$ of the former volume

Option 3: increased by $\frac{1}{8}$ of the former volume

Option 4: reduced by $\frac{1}{8}$ of the former volume

Question : Directions: The price of an article has been reduced by 25%. To restore the original price, the new price must be increased by?

Option 1: $11\frac{1}{9}\%$

Option 2: $66\frac{2}{3}\%$

Option 3: $9\frac{1}{11}\%$

Option 4: $33\frac{1}{3}\%$

Question : What is the value of $\frac{x^2-x-6}{x^2+x-12}÷\frac{x^2+5x+6}{x^2+7x+12}$?

Option 1: $1$

Option 2: $\frac{(x-3)}{(x+3)}$

Option 3: $\frac{(x+4)}{(x-3)}$

Option 4: $\frac{(x-3)}{(x+4)}$

Question : What is the simplified value of $(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x-\frac{1}{x})(x^{16}+\frac{1}{x^{16}})(x+\frac{1}{x})(x^{4}+\frac{1}{x^{4}})?$

Option 1: $(x^{64}+\frac{1}{x^{64}})$

Option 2: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$

Option 3: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x+\frac{1}{x})}$

Option 4: $\frac{(x^{32}-\frac{1}{x^{32}})}{(x+\frac{1}{x})}$

Question : If the numerator of a fraction is increased by 60% and the denominator is increased by 40%, then the resultant fraction is $\frac{16}{63}$. The original fraction is:

Option 1: $\frac{5}{9}$

Option 2: $\frac{2}{9}$

Option 3: $\frac{2}{11}$

Option 4: $\frac{4}{9}$