Question: A librarian has added 8 new books to his library for the past 40 days. On the 41st day, he removed 280 old books. After removal of these books, the total number of books was 6,000. Find the number of books that were there in the library initially.
A ) 5,000 B ) 6,500 C ) 6,000 D ) 5,960
Steps to derive
7 Let the number of books in the library initially be c.
8 Librarian added 8 books everyday for 40 days.
9 So, the number of new books added to the library in 40 days = 40(8) = 320.
10 The number of books removed by the librarian on the 41st day from the library which are too old = 280.
11 After the removal of these books, the number of remaining books in the library = 6,000
12 So, c + 320 - 280 = 6000 [Algebraic model.]
13⇒c = 5960. [Solve for c.]
14 The initial number of books in the libray = 5,960.
