Question

Guru reads $\dfrac{3}{5}$ of a book. He finds that there are still $80$ pages left to be read. Total number of pages in the book are
A) $100$
B) $200$
C) $300$
D) $400$

Answer 1

Hint: We can assume the total number of pages in the book will be $x$. And given that Guru read $\dfrac{3}{5}$ of a book. So, number of pages read by Guru would be $\dfrac{3}{5}x$
So, remaining pages are given $80$ pages left. As total pages were $x$ and he read $\dfrac{3}{5}x$ , so you can find the number of pages yet to be read or left and equate it to $80$. You will get the value of $x$.

Complete step-by-step answer:
According to the question, Guru reads $\dfrac{3}{5}$ of a book and after reading these many pages, he finds that there are still $80$ pages left to be read. So, now we need to find the total number of pages in the book.
Let us consider the total number of pages in the book to be $x$ .
So, as we know, Guru read $\dfrac{3}{5}$ of the book.
So, the number of pages read by Guru$ = \dfrac{3}{5}x$
And we know total number of pages we assumed to be $x$
So, out of $x$ , Guru read $\dfrac{3}{5}x$ number of pages.
So, we can find the number of pages left to be read$ = x - \dfrac{{3x}}{5}$
So, number of pages left to be read by Guru$ = x - \dfrac{{3x}}{5}$
Here, $x$ is the total number of pages and $\dfrac{3}{5}x$ is the number of pages Guru already read.
So, we can calculate the number of pages left by Guru to read
$
   = x - \dfrac{{3x}}{5} \\
   = \dfrac{{5x - 3x}}{5} \\
   = \dfrac{{2x}}{5} \\
 $
Now, as in the question, we are given that Guru still has to read $80$ pages, that means the number of pages left by Guru to read is given, that is, $80$.
And we calculated that $\dfrac{{2x}}{5}$ number of pages are left by Guru to read. So, both must be equal. So, equating both, we will get
$
  \dfrac{{2x}}{5} = 80 \\
  x = \dfrac{{80 \times 5}}{2} \\
  x = 200 \\
 $
So, we get $x = 200$
Therefore, total number of pages are $200$

So, option B is correct.

Note: We can do it like this also, that let total pages be $x$ and as he read $\dfrac{3}{5}$ of total pages and that $80$ pages are left to read, so,
$\dfrac{{3x}}{5} + 80 = x$.
Here $\dfrac{{3x}}{5}$ are the number of pages he has read and $80$ is the number of pages left to read. Both when added gives the total number of pages.