Little confused by your question shoppergal. What do you mean by "the original amount" and what do you mean by "the newly transferred amount"? What do you mean by "reducing the amount you owe at the normal rate" too? The last sentence isn't clear.
Like Blackberry said, if you have transferred a balance to a new card, generally repayments are against that first so any new transactions you make with the new card will attract interest at the card rate and will not be repaid until the underlying balance is cleared (thereby building up a nice tot of interest for the card provider).