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Chapter 5: Problem 38

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? (a) \(4.16 \%\) (b) \(5 \%\) (c) \(6.66 \%\) (d) none of these

Short Answer

Expert verified
a) 4.16 % b) 3.22 % c) 2.58 % d) 5.21 % Answer: a) 4.16 %

Step by step solution

01

Find the total characters in the book

First, we need to determine the total number of characters in the entire book. This can be found by multiplying the number of pages, lines per page, and characters per line: Total characters = pages 脳 lines per page 脳 characters per line Total characters = 30 pages 脳 25 lines/page 脳 35 characters/line = 26250 characters
02

Determine the characters per page in the new notebook

Next, calculate the total number of characters that can be written on a single page of the new notebook. This can be found by multiplying the number of lines per page and the characters per line for the new notebook: Characters per page in the new notebook = Lines per page 脳 Characters per line Characters per page in the new notebook = 30 lines/page 脳 28 characters/line = 840 characters/page
03

Calculate the number of pages required in the new notebook

Now, divide the total number of characters in the book by the total characters per page in the new notebook to find the number of pages required to fit all the content: Number of pages in the new notebook = Total characters 梅 Characters per page in the new notebook Number of pages in the new notebook = 26250 characters 梅 840 characters/page = 31.25 pages
04

Compare the number of pages

The new notebook will require more pages than the initial book, 31.25 pages compared to the original 30 pages. To find the percentage of the increase in pages, use this formula: Percentage increase = ((New number of pages - Initial number of pages) 梅 Initial number of pages) 脳 100 Percentage increase = ((31.25 pages - 30 pages) 梅 30 pages) 脳 100 = 1.25 pages 梅 30 pages 脳 100 = 4.16 % The correct answer is (a) 4.16 %.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Arithmetic Calculations
Arithmetic calculations are the foundation of solving percentage increase problems. In this exercise, arithmetic is used to find the total number of characters in a book. Here's how:
  • Multiply the number of pages by the number of lines per page.
  • Multiply the result by the number of characters per line.
This gives the total number of characters in the book. For our example, it is:\[30 \text{ pages} \times 25 \text{ lines/page} \times 35 \text{ characters/line} = 26250 \text{ characters}.\]Arithmetic operations are efficient for performing basic calculations like additions, subtractions, multiplications, and divisions, each of which can help break down larger problems into manageable steps. By mastering these, solving problems like the one above becomes much more straightforward.
Mathematical Reasoning
Mathematical reasoning involves identifying the relationships between different elements of a problem and understanding how to apply formulas or concepts to find a solution. In this percentage increase problem:
  • We first reason that to find the increase in pages, we need to compare the total characters on a new layout versus the old.
  • We identify that finding the number of pages required depends not just on the total characters, but also on the new layout (lines per page and characters per line).
This leads to understanding that the number of characters per page in the new notebook affects the total pages required, influencing the percentage increase calculation. The reasoning guides you to:\[\text{Characters per page in the new layout} = 30 \text{ lines/page} \times 28 \text{ characters/line} = 840 \text{ characters/page}.\]It helps break down complex ideas into understandable parts, aiding in decision-making processes.
Ratio and Proportion
Ratio and proportion play a crucial role in understanding how one quantity changes in relation to another. In this problem:
  • We set up a ratio to compare the total number of pages needed in the old and new notebooks.
  • The comparison of the number of pages needed initially to those needed now forms a basis for a proportion calculation.
By dividing the total characters by characters per page in the new notebook, we find:\[\text{Number of pages in the new notebook} = \frac{26250 \text{ characters}}{840 \text{ characters/page}} \approx 31.25 \text{ pages}.\]Understanding this concept allows you to calculate the increase as a proportion of the original number of pages, showing the new notebook requires more than initially.
Quantitative Aptitude
Quantitative aptitude involves understanding and working with numbers to solve real-world problems. This problem is a great example of how quantitative aptitude is applied:
  • First, calculate essential totals, such as total characters in a book.
  • Use derived values to calculate required outputs, like the number of pages.
  • Finally, calculate percentage increase as: \( \frac{\text{New number of pages} - \text{Initial number of pages}}{\text{Initial number of pages}} \times 100 \).
For our exercise:\[\text{Percentage increase} = \left( \frac{31.25 \text{ pages} - 30 \text{ pages}}{30 \text{ pages}} \right) \times 100 = 4.16\%\]The numerical agility in calculations helps individuals solve such questions precisely. Therefore, practicing quantitative aptitude will sharpen problem-solving skills, enabling efficient work with data and calculations.

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