Nora had already read 30 % of the book before the teacher assigned it to the class She is choosing between two options to finish reading the book. .Option 1: read 25% pages each night . Option 2: read 28 pages each night Which option should Nora use to finish the book in the least amount of time? Nora has already read ? pages remaining in the book. Nora should choose option ? because it will take her ? nights to finish instead of ? nights with option ?

Let p represent the # of pages in the book.  Then, Nora has already read 0.30p pages and has 0.70p pages left to read.

If she reads 25% pages/night, that means reading 0.25(0.70)p pages per night, or 17.5 pages/night.  If 28% p/n, that means 0.28(0.70)p pages/night, or 19.6p pages/night.

How many nights will it take Nora to finish the book if she reads 25% of 7/10 of the book per night?  Without any calculations, we can answer this by "4 nights, since she reads 1/4 of the unread portion of the book per night."

If she reads 28% of 7/10 of the book per night, that will require fewer nights:
First night:  28%
Second night:  28% 
Third night:  28%
  Total:  3(28%) = 84%
This leaves 16% to read on the final night.

This is one interpretation of what I think is a poorly worded question.

The author of this question might have meant reading 25% of the remaining unread pages per night, which leads to a different answer.