A textbook has a total of 662 pages. It is divided into two parts. The second part of the book has 52 pages le

Question

A textbook has a total of 662 pages. It is divided into two parts. The second part of the book has 52 pages less than the first part. How many pages are there in the first part of the book?

Examoogle · Accepted Answer

The correct answer is Option D: 357. If the sum ($S$) and difference ($D$) of two quantities are known, the larger quantity is given by $(S + D)/2$. Here, Total pages is the sum of the two parts and the difference is 52.

Step-by-Step Solution & Concepts:
Shortcut Trick: If the sum ($S$) and difference ($D$) of two quantities are known, the larger quantity is given by $(S + D)/2$. Here, Total pages is the sum of the two parts and the difference is 52.

Formula Used: $$	ext{First Part} = \frac{	ext{Total} + 	ext{Difference}}{2}$$

Given: Total pages = 662, Difference between second part and first part = 52 pages

Steps: Step 1: Set up the algebraic equations: Let the number of pages in the first part be $x$. Since the second part has 52 pages less than the first, the second part is $x - 52$. The total pages in the book is 662.. Step 2: Simplify the equation: Combine like terms on the left side of the equation.. Step 3: Solve for $x$: Add 52 to both sides of the equation, then divide by 2.

Answer: D is correct because the first part contains 357 pages, which satisfies the condition that the second part has $357 - 52 = 305$ pages and their total is $357 + 305 = 662$ pages.

Exam Tip: Such linear simultaneous word problems frequently appear in RRB and SSC quantitative aptitude tests under age and number-based problems.

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