How Many Pages Are in the Book? Solving Fractional Reading Problems

Solving puzzles and word problems can be fun, especially when they involve fractions and mathematics. For instance, letrsquo;s consider the problem of determining the number of pages in a book, when we know certain fractions of the book have been read. This article will guide you through the solution to the following problem: Mohan read 1/4th of a book. If he read further 91 pages, he would have read 3/5th of the book. How many pages were there in the book? Letrsquo;s break it down step-by-step.

Step-by-Step Solution

First, letrsquo;s denote the total number of pages in the book as x. According to the problem, Mohan read 1/4 of the book, which can be written as:

```math frac{1}{4} x ```

After reading these pages, he read an additional 91 pages and then had read 3/5 of the book. This means the total number of pages he had read after the additional 91 pages can be expressed as:

```math frac{1}{4} x 91 frac{3}{5} x ```

To solve this equation, we need to eliminate the fractions by finding a common denominator. The least common multiple of 4 and 5 is 20. Multiplying the entire equation by 20 to clear the fractions:

```math 20 left(frac{1}{4} x 91right) 20 left(frac{3}{5} xright) ```

This simplifies to:

```math 5x 1820 12x ```

Next, we rearrange the equation to isolate x:

```math 1820 12x - 5x ```

Simplifying gives:

```math 1820 7x ```

Dividing both sides by 7:

```math x frac{1820}{7} 260 ```

Therefore, the total number of pages in the book is 260 pages.

Alternative Approach: Using Fractions Directly

Alternatively, we can solve this problem using fractions directly. After reading 1/4 of the book, 3/4 of the book remains. If reading an additional 91 pages results in reading 3/5 of the book, then 2/5 of the book must be 91 pages. This is because 3/5 - 1/4 7/20 10/20 17/20 - 12/20 5/20 1/4, hence:

```math frac{2}{5} 91 ```

To find the total number of pages in the book, we can rearrange:

```math 1 frac{91 times 5}{2} 232.5 ```

Since the number of pages must be a whole number, the solution using fractions directly suggests there might be a mistake in the problem setup, unless the book has a non-integer number of pages, which is unrealistic. Thus, the most practical solution is the first one, giving us 260 pages.

Understanding the Problem

The problem also highlights some logical steps to consider in solving such puzzles:

Identify the known fractions and the corresponding pages read. Recognize the relationship between the fractions and the additional pages read. Use algebra to form and solve the equation. Double-check the solution using logical verification.

By following these steps, you can solve similar fractional reading problems and understand the underlying mathematical principles.

Related Keyword Analysis

When searching for problems like this, you can use the following keywords:

book pages: Understand how to calculate the pages in a book using fractions. fractional reading: Learn about solving problems involving fractions of a whole. algebraic problem: Get tips and techniques for solving algebraic puzzles and word problems.