Karthik read 613 th of a book in 1st week and 59 th of the remaining book in 2nd week. If there were 100 pages unread after 2nd week, how many pages were there in the book ?

Let the total book be 1

Then, in the 1st week $\frac{6}{13}$th of book is read

i.e remaining pages =   $1-\frac{6}{13}=\frac{7}{13}$

in 2nd week he read $\frac{5}{9}$th of it

i.e $\frac{5}{9}\times \frac{7}{13}=\frac{35}{117}$
Remaining pages after 2nd week =  $\frac{7}{13}-\frac{35}{117}=\frac{28}{117}$

But given remaining pages after 2nd week = 100

$\frac{28x}{117}=100$

--> x = 418 

 The total pages in the book are 418