Question

I read 4/9 of a book on one day and 3/5 of the remaining next day.If 100 pages of the book where still left unread, how many pages did the book contain

Answer 1

Let the book contains x number of pages.
Number of pages read on first day $=\frac{4}{9}\mathrm{x}$
Number of pages that remain unread after first day $=\mathrm{x}-\frac{4}{9}\mathrm{x}=\left(1-\frac{4}{9}\right)\mathrm{x}=\frac{5}{9}\mathrm{x}$
As the number of pages read on the second day is $\frac{3}{5}$ of the remaining pages after first day.
Therefore number of pages read on second day $=\frac{3}{5}\times \frac{5}{9}\mathrm{x}=\frac{1}{3}\mathrm{x}$
Total number of pages read = (number of pages read on first day + number of pages read on second day)
$=\frac{4}{9}\mathrm{x}+\frac{1}{3}\mathrm{x}=\left(\frac{4}{9}+\frac{1}{3}\right)\mathrm{x}=\frac{7}{9}\mathrm{x}$
Number of pages remaining unread after second day $$\begin{gathered} =\mathrm{x}-\frac{7}{9}\mathrm{x}=\frac{2}{9}\mathrm{x}=100............\left(\mathrm{Given}\right) \\ \mathrm{Therefore},\frac{2}{9}\mathrm{x}=100\Rightarrow \mathrm{x}=100\times \frac{9}{2}=450. \\ \mathrm{Hence}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{pages}\mathrm{in}\mathrm{the}\mathrm{book}\mathrm{is}450. \end{gathered}$$