This is from Gleim. Can someone better explain the solution please?

Ques- JD sells to retail stores on credit term of 2/10 N30. Daily average sales is 45,000. 60% of the customer take discount and pay on the 10th day while the rest pay on the 30th day, the amount of JD accounts receivable is

Correct ans- 810,000

Sol: 30days sale = 45,000*30 = 1,350,000.

40% or 540,000 is uncollected bc's cust do not take discount. The remaining 60% or 810,000 will be paid within the discount period. However, by the end of 30th day, only 2/3 of the 810,000 will be collected bc's the sales from 21st day through 30 are still within the discount period. (????) Therefore additional (810,000-540,000) will still be uncollected after 30th day but still be subjected to discount. In total the average receivable balance is 810,000 consisting of 540,000 and 270,000 that will be paid within the discount period.

Thanks in advance!

Every day during the month 45,000 is hitting accounts receivable; assume 30 days in a month.  45,000 billed each day is an increase of 1,350,000 for any given month (45,000 * 30).

The question is really asking what the average receiable balance would be on any given day, so the 30 day period keeps rolling.  Every day 45,000 of new charges come on accounts receivable and payments for 45,000 of previous charges come off.  The amount being paid is comprised of 18,000 from those who owe you from 30 days ago and 27,000 from those who owe you from 10 days ago. 

A "base" accounts receivable exists because for the very first month the A/R existed, it was increased by 1,350,000 and decreased by a portion of the payments for customers paying within the discount period.  60% of the payments for the 1,350,000 increase in A/R are received within the discount period.  However, for the first month, the decrease to A/R for those payments would only be for 20 days; payments received for increases to A/R during the last 10 days of the month would fall into the next month.  40% of the payments for the 1,350,000 increase to A/R fall into the next month entirely.  So, the decrease to A/R for the first month would be 540,000 (1,350,000 x 60% x 20/30).  1,350,000 - 540,000 = 810,000.  Once you hit the beginning of the second month, the A/R would continue to roll as described above.

Hope this helps!