A page contains 60 lines. A chapter contains 125 pages. A book contains 5 chapters. 20 such books form a bound. If there are total 30 lakh lines in an x number of bounds then the value of x is :

Options

A. 4
B. 2
C. 5
D. 6

Answer

To find the value of \( x \) (the number of bounds), we will calculate the total number of lines in one bound and then determine how many bounds are needed to reach a total of 30 lakh lines.

### Step 1: Calculate the number of lines in one page
Each page contains 60 lines.

### Step 2: Calculate the number of lines in one chapter
A chapter contains 125 pages. Therefore, the total number of lines in one chapter is:
\[ \text{Lines in one chapter} = \text{Number of pages in a chapter} \times \text{Lines per page} = 125 \times 60 \]

Calculating this:
\[ 125 \times 60 = 7500 \text{ lines} \]

### Step 3: Calculate the number of lines in one book
A book contains 5 chapters. Therefore, the total number of lines in one book is:
\[ \text{Lines in one book} = \text{Number of chapters in a book} \times \text{Lines in one chapter} = 5 \times 7500 \]

Calculating this:
\[ 5 \times 7500 = 37500 \text{ lines} \]

### Step 4: Calculate the number of lines in one bound
One bound contains 20 books. Therefore, the total number of lines in one bound is:
\[ \text{Lines in one bound} = \text{Number of books in a bound} \times \text{Lines in one book} = 20 \times 37500 \]

Calculating this:
\[ 20 \times 37500 = 750000 \text{ lines} \]

### Step 5: Calculate the number of bounds needed for 30 lakh lines
We know that 30 lakh lines equals 3000000 lines. To find the number of bounds \( x \), we use the formula:
\[ x = \frac{\text{Total lines}}{\text{Lines in one bound}} = \frac{3000000}{750000} \]

Calculating this:
\[ x = \frac{3000000}{750000} = 4 \]

Thus, the value of \( x \) is 4.

### Final Answer
The value of \( x \) is \( 4 \).

---