The correct option is
A because of this
Option B - 'Because' is used to explain a reason. For example, 'I am sick because I ate junk food.' As the given sentence doesn't explain reasons, we can't use 'because' here. Thus option B is incorrect.
Option C - 'This is because' is used to give an explanation of a situation. For example, 'I failed the exam. This is because I didn't study.' The given sentence doesn't give an explanation but explains the consequence of having a bad cold. Hence, we can't use 'this is because'. Thus option C is incorrect.
Option D - 'Owing to' means 'because of'. For example, 'His reading was hesitant owing to a stammer.' As 'Mrs. Dev' didn't lose her voice because of the bad cold, we can't use 'because of' here. Thus option D is incorrect.
Option A - 'Because of this' is used to explain the consequence or result of something. For example, 'I ate junk food, because of this my stomach is upset.' As the given sentence explains the result of something, we can use 'because of this' here. Thus option A is the correct answer.
'Mrs. Dev had a bad cold, because of this she lost her voice.'