A man reads three sevenths of a book on the first day and two fifths of the remaining part on the second day. If 36 pages of the book still remain unread, how many pages does the book contain in total?

Introduction / Context:
This problem is about reading fractions of a whole on different days. It checks your understanding of operations with fractions and how to work backwards from the remaining part to the total quantity.

Given Data / Assumptions:

• Let the total number of pages in the book be N.• On day one, the man reads three sevenths of the book.• On day two, he reads two fifths of the remaining pages.• After two days, 36 pages remain unread.• We must find the value of N.

Concept / Approach:
First, compute the remaining fraction of the book after the first day. Then apply the second day reading fraction to that remainder. The final remainder is given as a specific number of pages. We convert this relation into an equation in N and solve.

Step-by-Step Solution:
Step 1: Pages read on day one = (3/7) * N.Step 2: Remaining pages after day one = N − (3/7)N = (4/7)N.Step 3: On day two he reads two fifths of the remaining pages, that is (2/5) * (4/7)N = (8/35)N.Step 4: Pages remaining after day two = (4/7)N − (8/35)N.Step 5: Convert to common denominator 35: (4/7)N = (20/35)N, so remaining = (20/35 − 8/35)N = (12/35)N.Step 6: This remaining amount equals 36 pages.Step 7: So (12/35)N = 36, hence N = 36 * (35/12).Step 8: Simplify: 36/12 = 3, so N = 3 * 35 = 105.

Verification / Alternative check:
Check directly. Three sevenths of 105 is 45 pages, so 60 remain. Two fifths of 60 is 24, leaving 36 pages unread. This matches the given condition, confirming that 105 pages is correct.

Why Other Options Are Wrong:
Values 101, 98 and 109 do not produce a remaining count of 36 when the same fractional reading steps are applied. They arise from arithmetic errors with fractions or from subtracting fractions incorrectly.

Common Pitfalls:
A typical mistake is to apply two fifths to the original number of pages instead of the remaining pages. Another issue is failing to convert fractions to a common denominator when subtracting them.

Final Answer:
The book contains 105 pages in total.