​$$\text{Simplify } 1.\overline{45} + 0.3\overline{12} - 1.11\overline{2}.$$​​​

Correct option is A

Given:

$$1.\overline{45} + 0.3\overline{12} - 1.11\overline{2}.$$

Solution:

$$1.\overline{45} + 0.3\overline{12} - 1.11\overline{2}.$$

=  $$\left(1+ \frac{45}{99} \right)$$ + $$\left( \frac{312-3}{990} \right)$$ -$$\left( 1+\frac{112-11}{900} \right)$$

=$$\left( \frac{144}{99} \right)$$+ $$\left( \frac{309}{990} \right)$$- $$\left( 1+\frac{101}{900} \right)$$

=$$\left( \frac{144}{99} \right)$$+$$\left( \frac{309}{990} \right)$$-$$\left( \frac{1001}{900} \right)$$

=$$\left( \frac{14400+3090-11011}{9900} \right)$$

=$$\left( \frac{6479}{9900} \right)$$=$$\frac{589}{900}$$

Option (a) is right answer.