A boy read three-eighth of a book on one day and four-fifth of the remainder of the book on the next day. If 45 pages still remain unread, how many pages does the book contain?

Correct option is C

Given:

A boy reads $$\frac{3}{8}$$​ of the book on the first day.

On the next day, he reads $$\frac{4}{5}$$​ of the remainder of the book.

After reading, 45 pages remain unread.

Solution:

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

Pages read on the first day =$$\frac{3}{8}x$$​​

Pages remaining after the first day = $$x - \frac{3}{8}x = \frac{5}{8}x$$​​

Pages read on the second day = $$\frac{4}{5} \times \frac{5}{8}x = \frac{4}{8}x = \frac{1}{2}x$$​​

Now, 

$$\frac{5}{8}x - \frac{4}{8}x = 45$$​​

​$$\frac{1}{8}x = 45$$​

x = $$45 \times 8 = 360$$​

Thus, the total number of pages in the book is 360.