On a shelf, books with green cover and that with brown cover are in the ratio 2:3. If there are 18 books with green cover, then the number of books with brown cover is

Options

A. 12
B. 24
C. 27
D. 36

Answer

To solve the problem step by step, we will follow the given ratio and the information provided.

### Step 1: Understand the Ratio
The ratio of books with green covers to books with brown covers is given as 2:3. This means that for every 2 green books, there are 3 brown books.

**Hint**: Remember that ratios represent a relationship between two quantities.

### Step 2: Assign Variables
Let the number of green books be represented as \( G \) and the number of brown books as \( B \). According to the ratio, we can express this as:
\[ \frac{G}{B} = \frac{2}{3} \]

**Hint**: Use variables to represent quantities in a ratio for easier calculations.

### Step 3: Use the Given Information
We know that there are 18 green books. So, we can substitute \( G \) with 18:
\[ G = 18 \]

**Hint**: Substitute known values into your equations to simplify them.

### Step 4: Set Up the Equation
Now, substituting the value of \( G \) into the ratio:
\[ \frac{18}{B} = \frac{2}{3} \]

**Hint**: This equation allows you to find the unknown quantity by cross-multiplying.

### Step 5: Cross Multiply
Cross-multiplying gives us:
\[ 18 \times 3 = 2 \times B \]
This simplifies to:
\[ 54 = 2B \]

**Hint**: Cross-multiplication is a useful technique when dealing with ratios.

### Step 6: Solve for \( B \)
Now, divide both sides by 2 to find \( B \):
\[ B = \frac{54}{2} = 27 \]

**Hint**: Isolate the variable to find its value.

### Conclusion
The number of books with brown covers is 27.

**Final Answer**: There are 27 books with brown covers.