Question

Reema read $\frac{1}{5}$th pages of a book. If she reads further $40$ pages, she would have read $\frac{7}{10}$th pages of the book. How many pages are left to be read$?$

Answer 1

Step-1 Finding total number of pages:

Reema read ${\frac{1}{5}}^{th}$ pages of a book.

Let us assume the total number of pages in the book be$\text{T}$.

Then, the number of pages read by Reema $={\frac{1}{5}}^{th}\text{of T}$$=\left(\frac{1}{5}\right)\times T$

And also it is given in the question, If she reads further $40$ pages, she would have read ${\frac{7}{10}}^{th}$pages of the book. =$\left(\frac{7}{10}\right)\times T$

So, according to the question

$$\begin{gathered} \Rightarrow \left(\frac{1}{5}\times T\right)+40=\frac{7}{10}\times T \\ \Rightarrow \frac{T}{5}+40=\frac{7T}{10} \\ \Rightarrow \frac{T+200}{5}=\frac{7T}{10} \end{gathered}$$

By cross multiplication we get,

$\Rightarrow 10T+2000=35T$

$\Rightarrow 2000=35T-10T$

$\Rightarrow 2000=25T$

$\Rightarrow T=\frac{2000}{25}$

$\Rightarrow T=80$

Step-2 Finding number of pages left to read

Then, pages left to be read by Reemu = Total pages – pages read

$$\begin{gathered} =T–\frac{7T}{10} \\ =\frac{10T-7T}{10} \\ =\frac{3T}{10} \\ =\frac{3\times 80}{10}\mathbf{}\mathbf{(}\mathbf{Putting}\mathbf{}\mathbf{the}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{T}\mathbf{=}\mathbf{80}\mathbf{)} \\ =24 \end{gathered}$$

Therefore,$\mathbf{24}$ pages are left to be read.