If A = $$0.3\overline {12} ,$$  B = $$0.4\overline {15} $$  and C = $$0.30\overline 9 ,$$  then what is the value of A + B + C?

Solution (By Examveda Team)

$$\eqalign{ & A = 0.3\overline {12} = \frac{{312 - 3}}{{990}} = \frac{{309}}{{990}} \cr & B = 0.4\overline {15} = \frac{{415 - 4}}{{990}} = \frac{{414}}{{990}} \cr & C = 0.30\overline 9 = \frac{{309 - 30}}{{900}} = \frac{{279}}{{900}} \cr & A + B + C = \frac{{309}}{{990}} + \frac{{414}}{{990}} + \frac{{279}}{{900}} \cr & = \frac{{3090 + 4140 + 3069}}{{9900}} \cr & = \frac{{10269}}{{9900}} \cr & = \frac{{1141}}{{1100}} \cr} $$