If the cost of printing a book of 320 leaves with 21 lines on each page and on an average 11 words in each line is 19 , find the cost of printing a book with 297 leaves, 28 lines on each page and 10 words in each line.

Options

A. `'22(3)/(8)`
B. `'20(3)/(8)`
C. `'21(3)/(8)`
D. `'21(3)/(4)`

Answer

To solve the problem step by step, we will first calculate the total number of words in both books and then find the cost of printing the second book based on the cost of the first book.

### Step 1: Calculate the total number of words in the first book
The first book has:
- 320 leaves
- 21 lines on each page
- 11 words in each line

Total number of words in the first book can be calculated as:
\[ \text{Total words} = \text{Number of leaves} \times \text{Number of lines per page} \times \text{Number of words per line} \]
\[ \text{Total words} = 320 \times 21 \times 11 \]

### Step 2: Calculate the total number of words in the second book
The second book has:
- 297 leaves
- 28 lines on each page
- 10 words in each line

Total number of words in the second book can be calculated similarly:
\[ \text{Total words} = \text{Number of leaves} \times \text{Number of lines per page} \times \text{Number of words per line} \]
\[ \text{Total words} = 297 \times 28 \times 10 \]

### Step 3: Find the cost per word for the first book
The cost of printing the first book is 19. Therefore, the cost per word can be calculated as:
\[ \text{Cost per word} = \frac{\text{Total cost}}{\text{Total words in first book}} \]
\[ \text{Cost per word} = \frac{19}{320 \times 21 \times 11} \]

### Step 4: Calculate the cost of printing the second book
Using the cost per word calculated in Step 3, we can find the cost of printing the second book:
\[ \text{Cost of second book} = \text{Total words in second book} \times \text{Cost per word} \]
\[ \text{Cost of second book} = (297 \times 28 \times 10) \times \left(\frac{19}{320 \times 21 \times 11}\right) \]

### Step 5: Simplify the expression
Now we can simplify the expression to find the final cost of printing the second book.

### Final Calculation
1. Calculate the total words in the first book:
\[ 320 \times 21 \times 11 = 73920 \]
2. Calculate the total words in the second book:
\[ 297 \times 28 \times 10 = 83160 \]
3. Calculate the cost per word:
\[ \text{Cost per word} = \frac{19}{73920} \]
4. Calculate the cost of the second book:
\[ \text{Cost of second book} = 83160 \times \frac{19}{73920} \]
\[ = \frac{83160 \times 19}{73920} \]

Now calculating the above expression gives us the cost of printing the second book.