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Solutions
Correct option - 3
If we use 'has been teaching', this needs a time expressing word for this particular clause. But, here, no time expressing word is mentioned. Hence, option 5 is eliminated.
Also, 'since' is used for a particular time. Here, 'a month' is given, this is a time-period. Hence, use for in place of since.
Thus, options 1 & 4 are eliminated.
If we use 'would teach', it shows past tense. But 'nowadays' shows present tense. Hence, option 2 is eliminated.
Thus, option 3 i.e. teaches, himself for is the correct answer.