Though I have been paying off bills, credit cards, car installment etc timely, my scores are going down and down. I had recently applied for a credit card, this might be one reason to pull the score down, but am wondering how come the scores are precipitating so largely. In a span of one month, the scores came down by almost 50 points. 

Applying one credit card doesnt reduce your score by 50 marks. It does reduce score marginally. Check your credit history and try to find out if there are some mistake like  posted in ur credit report. Check all three credit score and report. Compare if they are more or less similar.