Question

Geeta read $\dfrac{4}{9}$ of a book on one day and $\dfrac{3}{5}$of the remaining the next day. If 100 pages of the book were still left unread, how many pages did the book contain ?

Answer 1

Hint: whenever we say a fraction is “OF” a something it means multiplication . Take an unknown variable $x$ and express the amount pages Geeta read on the first and second day in $x$. Sum the total with unread pages and solve the equation.

Complete step-by-step answer:
We know from the fraction that a fractional part of total expressed is in multiplication. When we say that $\dfrac{a}{b}$ parts of $c$ then it means $\dfrac{a}{b}\times c$. \[\]
It is given in the question that Geeta read $\dfrac{4}{9}$ of a book on one day and $\dfrac{3}{5}$ of the remaining book the next day.\[\]
 Let us assume that the total number of pages in the book is $x$. So Geeta reads in the first day is $\dfrac{4}{9}$ of the total pages or $\dfrac{4}{9}$ of $x$ which is $\dfrac{4}{9}x$ number of a pages. \[\]
The number of pages remaining is the difference between total numbers of pages and the numbers of pages Geeta has already read that is $x-\dfrac{4}{9}x=\dfrac{9x-4x}{9}=\dfrac{5}{9}x$\[\]
Geeta read on the second day is $\dfrac{3}{5}$ of the remaining part. The remaining part is $\dfrac{5}{9}x$ number of pages. So Geeta read $\dfrac{3}{5}$ of $\dfrac{5}{9}x$ that is $\dfrac{3}{5}\times \dfrac{5}{9}x=\dfrac{3}{9}x=\dfrac{1}{3}x$ number of pages in second day.\[\]
It is also given that 100 pages were left unread . So that means the total number of pages that is $x$ is the sum of number of pages Geeta read in first that is $\dfrac{4}{9}x$ , second day that is $\dfrac{1}{3}x$ and did not read that is 100 pages. . We can express it as
\[\begin{align}
  & \dfrac{4}{9}x+\dfrac{1}{3}x+100=x \\
 & \\
\end{align}\]
Let us multiply 9 with each term in above equation and get,
\[\begin{align}
  & 4x+3x+900=9x \\
 & \Rightarrow 7x+900=9x \\
\end{align}\]
We subtract $7x$ from both side of the equation and get \[\dfrac{{}}{{}}\]
\[\begin{align}
  & \Rightarrow 900=2x \\
 & \Rightarrow x=\dfrac{900}{2}=450 \\
\end{align}\]
So the total number of pages is 450.

Note: The key word in this question is “remaining”. Geeta on the second day is not going to read again from the beginning and that is why we need to find out how many pages Geeta read of the remaining pages not total in the second day.