Question

If 6 books are to be arranged in 2 shelves in a library,


what is/are the correct way(s) of arranging them so that each shelf has equal number of books?

• A. Each shelf has: $(4÷2)+(2÷2)$ books
• B. Each shelf has: $(6÷2)$ books
• C. Each shelf has: $(4÷2)+(2÷1)$ books
• D. Each shelf has: $(2÷2)+(2÷2)+(2÷2)$ books

Answer 1

Answer: (A), (B), (D)

The correct options are
A Each shelf has: $(4÷2)+(2÷2)$ books
B Each shelf has: $(6÷2)$ books
D Each shelf has: $(2÷2)+(2÷2)+(2÷2)$ books

According to the question:

• There are 6 books
• They are to be kept equally in 2 shelves.

We can make different groups of these books to divide them among the shelves.

$\ast \text{1st group}:$ (4 books + 2 books)
If we divide first 4 books in 2 shelves which is:
4$÷$2 = 2 books.
So, 6 - 4 = 2 books are remaining.
These 2 books are again to be divided in the 2 shelves which is:
2$÷$ 2 = 1 book each.
$\therefore$ Each shelf will have 2 + 1 = 3 books.

$\ast \text{2nd group}:$ (Full 6 books)
If we divide all the 6 books in 2 shelves which is:
6$÷$2 = 3 books.
$\therefore$ Each shelf will have 3 books.

$\ast \text{3rd group}:$ (2 books + 2 books + 2 books)
If we divide first 2 books in 2 shelves which is:
2$÷$2 = 1 book.
Similarly, if we repeat this process for the next 2 times, we get that
each shelf will have 1 + 1 + 1 = 3 books.

So, we see that all these ways of distribution can be used to divide 6 books in 2 shelves and at the end each shelf will have 3 books.

Also, if any group fails to give 3 books in each shelf then that group formation is not correct.