If a firm pays its bills with a 30 day delay, what fraction of its purchases will be paid for in the current quarter? The following quarter? What if its payment delay is 60 days

In interim period, costs that will not benefit other inteim peiod will be recorded in the perion where they occur. But if it is evident that the cost will benefit though whole year, it will be allocated over the other interim periods.

There are 4 quarters in the year.

So if you don't pay until the next month... (30 day delay)

Then you only pay for 2 months out of 3... (3 months to a quarter x 4 quarters = 12 months)

So 1/3 of purchases in the quarter are not paid in the quarter at 30 days.

2/3 of purchases in the quarter are paid in this quarter at 30 days.

For 60, that just adds another month to the future.
So, this quarter 1/3, next quarter 2/3