B because you could have ended the sentence there but you didn't. also if you use semicolons you don't need because. you would also not put i has before.
Sector 7,
Dwarka,
New Delhi
110006
Date- 16th August 2018
Dear Mother,
How are you? Everything is well at my end and hope the same with you. In this letter, I wanted to tell you about today as today was one of the most hectic days. Because of the Independence Day celebration, I was very tired since yesterday. And today my maths teacher had asked us to complete the assignment tomorrow itself. Although I've completed the task but have become very tired.
For now, I’m ending the letter. Will talk about it more in another letter. Take care of yourself.
Your loving son
XYZ
