The correct option is A 0.444....
Given operation is 0.111... + 0.333....
Let 'x' be 0.111....
Multilpy x with 10.
⇒ 10x = 1.11....
= 1 + 0.111....
= 1 + x (∵x=0.111....)
⇒ 9x = 1
⇒ x = 19
∴ 0.111.... = 19...............(1)
Now we can express 0.3 as 3 × 0.111....
∵ from (1), 0.111.... = 19
⇒0.333...=3×19
=39
∴ 0.333.... = 13
Now, 0.111... + 0.333.... = 19+13
= 49
49=4×19
∵19=0.111..... [from eq(1)]
⇒49=4×0.111... =0.444....
∴ 0.111... + 0.333.... = 0.444...