Question

A boy read $\dfrac{{{3}^{th}}}{8}$ of a book on one day and $\dfrac{{{4}^{th}}}{5}$ of the remaining on another day. If there were 30 pages unread, how many pages did the book contain?

Answer 1

Hint: To solve this question first we will find the number of pages read on both the days by assuming ‘x’ as the total number of pages contained in the book. We can then form equations using the data given in the question. For example we have been given that the boy reads ${{\dfrac{3}{8}}^{th}}$ of a book on one day, so we can say that he reads $\dfrac{3x}{8}$ pages of book and $x-\dfrac{3x}{8}$ pages are left to be read. Then, similarly we can form the next equation and simplify to get the value of x. We will find the numbers of remaining unread pages which are also given in question which will help us to find the total numbers of pages in the book.

Complete step-by-step answer:
Let us consider the total number of pages in the book to be ‘x’.
It is given in the question that a boy read ${{\dfrac{3}{8}}^{th}}$ of a book on day 1. Since we have ‘x’ number of pages in the book, we can say that the pages that the boy read on day 1 would be –
$\Rightarrow x\times \dfrac{3}{8}=\dfrac{3x}{8}$
Now, we can write that the remaining pages would be –
$=x-\dfrac{3x}{8}$
By taking the LCM, we get –
$\dfrac{8x-3x}{8}=\dfrac{5x}{8}$
It is also given that, On other day he read $\dfrac{{{4}^{th}}}{5}$ of remaining pages.
i.e. $\left( \dfrac{5x}{8} \right)\left( \dfrac{4}{5} \right)=\dfrac{20x}{40}$
$=\dfrac{x}{2}$
We can get the total numbers of pages read on both the days by adding the results as below -
$\dfrac{3x}{8}+\dfrac{x}{2}$
By taking the LCM of 8 and 2, which is 8, we get –
$\begin{align}
  & \Rightarrow \dfrac{3x}{8}\times 8+\dfrac{x}{2}\times 8 \\
 & =\dfrac{3x+4x}{8} \\
 & =\dfrac{7x}{8} \\
\end{align}$
Now, we will find the numbers of remaining pages unread. So, we can subtract it from x as,
$x-\dfrac{7x}{8}$
By taking LCM, we get –
$\dfrac{8x-7x}{8}=\dfrac{x}{8}$
According to the question the remaining unread pages are 30.
So, we can equate as $\dfrac{x}{8}=30$
By multiplying 8 on both sides, we get –
$x=240$
Hence, the total no. of pages in the book is 240.

Note: Students get confused while understanding the question. They need to be very careful while reading and understanding the question. Here in this question it is given that $\dfrac{{{4}^{th}}}{5}$ of the remaining book is read on other day, which means we have to find the numbers of pages read on other day by multiplying $\dfrac{{{4}^{th}}}{5}$ with remaining unread pages of the book.