Question

A boy reads \[\dfrac{3}{8}th\] of a book in one day and \[\dfrac{4}{5}th\] of the remaining in another day. If there were \[30\] unread pages. How many pages did the book contain?

Answer 1

Hint:To find the number of pages contained in the book, we assume that the number of pages in the book be \[x\]. So first we need to find the number of pages read in one day and then the number of pages read in the next day all in terms of \[x\].
After finding the number of pages read on the first day and other days in terms of \[x\], we find the value of \[x\] using the two equations giving us the value of the total number of pages. The formula for the total number of pages: \[\left( \text{Part read in Day One} \right)x+\text{Remaining Dfraction}\left( 1-\left( \text{Part read in Day One} \right) \right)x+\text{Unread Pages}=x\].

Complete step by step solution:
According to the question given. The fraction of a book, boy reads on day one is \[\dfrac{3}{8}\].
Assuming that the total number of pages of the book is given as \[x\], then the number of pages read by the boy in terms of \[x\] is \[\dfrac{3}{8}x\].
And the number of pages read by the boy another day in terms of \[x\] is given as \[\dfrac{4}{5}x\].
The fraction of book left after reading on the first day is written as
\[\left( 1-\dfrac{3}{8} \right)x\].
Now that we have the number of pages read both on first day and another day, and to put the value in the formula to find the value of the total number of pages in the book is:
\[\Rightarrow \left( \text{Part read in Day One} \right)x+\text{Remaining Fraction}\left( 1-\left(\text{Part read in Day One} \right) \right)x+\text{Unread Pages}=x\]
Placing the values in the above formula, we get the total number of pages (with the total number of unread pages as \[30\] pages ) as:
\[\Rightarrow \dfrac{3}{8}x+\dfrac{4}{5}\left( 1-\left( \dfrac{3}{8} \right) \right)x+\text{30}=x\]
Simplifying the fraction to find the total number of pages.
\[\Rightarrow \dfrac{3}{8}x+\dfrac{4}{5}\left( \dfrac{5}{8} \right)x+\text{30}=x\]
\[\Rightarrow \dfrac{3}{8}x+\dfrac{1}{2}x+\text{30}=x\]
Shifting the value from LHS to RHS, we get the value as:
\[\Rightarrow \dfrac{3}{8}x+\text{30}=\dfrac{1}{2}x\]
\[\Rightarrow \text{30}=\dfrac{1}{2}x-\dfrac{3}{8}x\]
Hence, the value of \[x\] when subtracting the RHS is:
\[\Rightarrow \text{30}=\dfrac{1}{6}x\]
\[\Rightarrow x=240\]
Therefore, the total number of pages in the book is equal to \[240\] pages.

Note: Let us assume that the book contains \[8\] pages.
Hence, on the first day the number of pages read is: \[\dfrac{3}{8}\times 8=3\] pages.
Therefore, the remaining pages are the total number of pages assumed subtracted by the pages read on the first day.
\[\Rightarrow 8-3=5\] pages.
And on the another day, the number of pages read is:
\[\Rightarrow \dfrac{4}{5}\times 5=4\] pages.
Therefore, the number of page left read in terms of fraction is:
\[3+4\] pages. If I page is left after reading \[8\] pages then if \[30\] pages are left then the book should have \[30\times 8\] pages.