A boy read $\frac{3}{8}$ th of a book on one day and $\frac{4}{5}$ th of the remainder on another day. If there were 30 pages unread, how many pages did the book contain?
(a)240
(b)300
(c)600
(d)None of these
Answer
Answer (as printed): A
Explanation
Part read on first day $=\frac{3}{8}$. Remaining part $=\left(1-\frac{3}{8}\right)=\frac{5}{8}$. Part read on second day $=\frac{4}{5}$ of $\frac{5}{8}=\frac{1}{2}$. Unread part $=\left[1-\left(\frac{3}{8}+\frac{1}{2}\right)\right]=\frac{1}{8}$. Let the number of pages be $x$. Then, $\frac{1}{8} x=30$ or $x=30 \times 8=240$.
Explanation as extracted from the printed page; notation may be imperfect.