Question

A boy read $\frac{3}{8}$ of book on one day and $\frac{4}{5}$ of the remainder on the other day.

If there were $30$ pages unread, how many pages did the book contain?

Answer 1

Solve for the total number of pages that the book contain:

Given that boy read $\frac{3}{8}$ of book on one day and $\frac{4}{5}$ of the remainder on the other day and $30$ pages were unread.

L.C.M. $\left(8,5\right)=40$

Let the total number of pages in the book be $40x$

According to the question,

Number of pages unread at the end of first day $=40x-\frac{3}{8}\left(40x\right)=25x$

Number of pages unread at the end of second day $=25x-\frac{4}{5}\left(25x\right)=5x$

$\therefore$ $5x=30$ [Given]

$$\begin{gathered} \Rightarrow x=6 \\ \Rightarrow 40x=240 \end{gathered}$$

Hence, the book contains $240$ pages