A book consists of 30 pages, 25 lines on each page and 35 characters on each line. If this content is written in another note book consisting of 30 lines and 28 characters per line, then the required no. of pages will how much per cent greater than the previous pages?

Options

A. `4.16%`
B. `5%`
C. `6.66%`
D. none of these

Answer

To solve the problem step by step, we will calculate the total number of characters in the original book and then determine how many pages would be needed in the new notebook format. Finally, we will find the percentage increase in the number of pages.

### Step 1: Calculate the total number of characters in the original book.

The original book has:
- 30 pages
- 25 lines per page
- 35 characters per line

Total characters = Number of pages × Lines per page × Characters per line

\[ \text{Total characters} = 30 \times 25 \times 35 \]

Calculating this:

\[ 30 \times 25 = 750 \]
\[ 750 \times 35 = 26250 \]

So, the total number of characters in the original book is **26,250**.

### Step 2: Calculate the number of pages required in the new notebook.

The new notebook has:
- 30 lines per page
- 28 characters per line

Total characters that can fit on one page of the new notebook:

\[ \text{Characters per page} = \text{Lines per page} \times \text{Characters per line} = 30 \times 28 \]

Calculating this:

\[ 30 \times 28 = 840 \]

Now, we need to find out how many pages are required to accommodate 26,250 characters:

\[ \text{Number of pages} = \frac{\text{Total characters}}{\text{Characters per page}} = \frac{26250}{840} \]

Calculating this:

\[ \frac{26250}{840} \approx 31.25 \]

Since we cannot have a fraction of a page, we round up to **32 pages**.

### Step 3: Calculate the percentage increase in the number of pages.

The original book had 30 pages, and the new notebook requires 32 pages.

To find the percentage increase:

\[ \text{Percentage increase} = \frac{\text{New pages} - \text{Original pages}}{\text{Original pages}} \times 100 \]

Substituting the values:

\[ \text{Percentage increase} = \frac{32 - 30}{30} \times 100 = \frac{2}{30} \times 100 \]

Calculating this:

\[ \frac{2}{30} \times 100 = \frac{200}{30} \approx 6.67\% \]

### Final Answer:
The required number of pages in the new notebook is approximately **6.67% greater** than the original pages.

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