Question

In shelf, the book with a green cover and that with brown cover is in the ratio $2:3$. There are 18 books with a green cover, then the number of books with brown cover is?
A) 12
B) 24
C) 27
D) 36

Answer 1

Hint: In this statement, we have to find the number of books in brown cover when the number of books having green cover is given. The approach for this statement is to assume the common factor i.e. x than green cover books will be 2x and brown cover books will be 3x.

Complete step by step solution: We are given the ratio of books having green cover and books having brown i.e. $2:3$
Let the number of books having green cover be 2x and therefore the number of books having brown cover is 3x.
As it is given the number of books having green cover is equal to 18.

$
   \Rightarrow 2x = 18 \\
   \Rightarrow x = \dfrac{{18}}{2} \\
$
$ \Rightarrow x = 9$ …………(1)


To find the number of books having a brown cover, you can directly solve by putting the value of x in 3x.

$ \Rightarrow N(B) = 3x$, where N(B) is the number of books having a brown cover.

From 1, $x = 9$

$
   \Rightarrow N(B) = 3 \times 9 \\
   \Rightarrow N(B) = 27 \\
$

The number of books having brown cover is 27. Option C is 27, hence it is the correct option.

So, option C is the correct option.


Note: If we want to find the total number of books having both green and brown cover. This can be done by calculating the total number of books in the shelf having green and brown cover.
$ \Rightarrow Total = N(G) + N(B)$, where N(G) is number of books having green cover. & N(B) is the number of books having a brown cover.

$
   \Rightarrow Total = 2x + 3x \\
   \Rightarrow Total = 5x \\
   \Rightarrow Total = 5 \times 9 = 45 \\
$

 Second approach to this question: The green cover book is $\dfrac{2}{5}$ of total. This can be calculated taking $\dfrac{2}{\begin{gathered}
  3 + 2 \\
    \\
\end{gathered} }$ and $\dfrac{3}{5}$we have to find
So, $
  \dfrac{2}{5} \to 18 \\
   \Rightarrow \dfrac{3}{5} \to \dfrac{{18}}{2} \times 3 = 9 \times 3 \\
   \Rightarrow N(B) = 27 \\
$