Reading a book in stages: A man reads 3/8 of a book on day one and 4/5 of the remainder on day two. If 40 pages are still unread, how many pages does the book contain?

Introduction / Context:
Sequential fraction reading problems test your ability to update the remainder after each step. The key is to carefully compute what remains after each day, then match the final remainder to the known number of unread pages to recover the total number of pages in the book.

Given Data / Assumptions:

• Day 1: reads 3/8 of the book.
• Day 2: reads 4/5 of the remainder from Day 1.
• Unread after Day 2 = 40 pages.

Concept / Approach:
Let the total number of pages be N. After reading 3/8, the remainder is 5/8 of N. On day two, he reads 4/5 of that remainder and leaves 1/5 of it unread. Convert these steps into a single fraction of N that remains, equate to 40, and solve for N.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 300, 350, 500: Do not yield 40 pages remaining after applying the same fractions; arithmetic check fails.

Common Pitfalls:

• Applying 4/5 to the total instead of the remainder.
• Confusing “remainder unread” with “remainder read.”

Final Answer: