If $A=0.\overline{2}$ and $B=0.\overline{21}$, then which of the following statements is correct?

The correct option is A $A>B$
Detailed step-by-step solution:
Here,
$A=0.\overline{2}=0.2222\dots$
$B=0.\overline{21}=0.2121\dots$

Both the decimals have the same digits before the decimal point.
As the digits before the decimal point are identical, we have to compare the first digit after the decimal point, which is the tenth digit.
Both the decimals have the same digits at tenths place.
By comparing the digits at hundredths place,
we can say that $0.22>\mathrm{0.21.}$
$\to 0.2222\dots >0.2121\dots$
$\to A>B$