A girl wants to finish reading a book. She reads 2/5 of the book on the first day, 34% of the book on the second day, and the remaining pages over the next two days in equal parts. If she reads 52 pages on the last day, how many pages are there in the book in total?

Introduction / Context:
This is a mixed fraction and percentage word problem that appears often in aptitude exams. The girl reads different portions of the book over several days, with the first portion expressed as a fraction, the second as a percentage, and the remaining portion split equally between two more days. We are told how many pages she reads on the last day, and from this we must determine the total number of pages in the book. This tests the ability to convert fractions and percentages into consistent forms and to track remaining quantities step by step.

Given Data / Assumptions:

Let the total number of pages in the book be P.

On day one she reads 2 / 5 of the entire book.

On day two she reads 34% of the entire book.

The remaining pages are read over the next two days in equal amounts.

On the last day she reads 52 pages, which equals half of the remaining pages after day two.

Concept / Approach:
We will first express all parts as fractions of the total number of pages. Two fifths is 0.4P and 34% is 0.34P. After these two days, the total proportion read is 0.4P + 0.34P, so the remaining proportion is 1 - (0.4 + 0.34). That remaining part is split equally into two equal portions, one for each of the last two days. Since the number of pages on the last day is given, we can set the last day pages equal to half of the remaining portion and solve for P.

Step-by-Step Solution:
Let the total number of pages be P.Pages read on day one = (2 / 5)P = 0.4P.Pages read on day two = 34% of P = 0.34P.Total pages read in first two days = 0.4P + 0.34P = 0.74P.Remaining pages after two days = P - 0.74P = 0.26P.This remaining 0.26P is read equally over the next two days, so each day she reads (0.26P) / 2 = 0.13P.Given that the pages read on the last day equal 52.So, 0.13P = 52.Therefore, P = 52 / 0.13 = 400.Thus, the book contains 400 pages.

Verification / Alternative check:
Verify by reconstructing the reading schedule using P = 400. Day one: 2 / 5 of 400 = 160 pages. Day two: 34% of 400 = 0.34 * 400 = 136 pages. Total after two days = 160 + 136 = 296 pages. Remaining pages = 400 - 296 = 104 pages. These 104 pages are split equally over days three and four, so each day the girl reads 52 pages. This matches the information that she reads 52 pages on the last day. Therefore, the calculated total of 400 pages is consistent.

Why Other Options Are Wrong:

525, 325, 475 and 450 do not satisfy the conditions when you repeat the calculation steps; the last day pages do not come out to 52.

For example, with 450 pages, the remaining portion after first two days would not divide into equal parts of 52 pages each.

Common Pitfalls:
Some learners mistakenly apply 34% to the remaining pages instead of the whole book. Others confuse the fraction 2 / 5 with 2 / 50 or misinterpret 34% as 0.034. Another common error is to forget that the last day pages represent exactly half of the remaining pages after day two. Writing every step in terms of P and carefully simplifying helps avoid these mistakes.

Final Answer:
The total number of pages in the book is 400.