Pls answer

meghamehta15 wrote:34. On Jane's credit card account, the average daily balance for a 30-day billing cycle is average (arithmetic mean) of the daily balances at the end of the 30 days. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was average daily balance on Jane's account for the billing cycle?

1). Jane's payment was credited on the 21st day of the billing cycle.

2). The average daily balance through the 25th day of the billing cycle was $540

Answer is D.

Card balance starts with $600. If we know when the payment is done then we can compute the average daily balance. Lets see what both statements say:
(1) If payment was credited on 21st day, it means that she had $600 for 20 days and from 21st to 30th day she had $300 in her account ($600 balance - $300 payment). So the average can be obtained from this much information. Mean = (600*20+300*10)/30

(2)if avergare thru 25th day is 540 then somewhere on the way she made the payment. Lets see if we can find it. if ith day was the one when $300 was credited to her account then 540 = (600*i + 300*(25-i))/25 solve the eqn for i. Then one can easily obtain the daily average like shown in (1)