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Reimu read $\frac{1}{5}$ pages of a book. If she reads further 40 pages, she would have read $\frac{7}{10}$ pages of the book. How many pages are left to be read?
Given :
Reimu read $\frac{1}{5}$ pages of a book.
If she reads further 40 pages, she would have read $\frac{7}{10}$ pages of the book.
To do :
We have to find the number of pages left to read.
Solution :
Let the number of pages of the book be x.
This implies,
$\frac{1}{5}(x) + 40 = \frac{7}{10}(x)$
$\frac{(x+40(5))}{5} = \frac{7x}{10}$
$\frac{(x+200)}{5} = \frac{7x}{10}$
$(x+200) = 5(\frac{7x}{10})$
$x+200 = \frac{7x}{2}$
$2(x+200) = 7x$
$2x+400 = 7x$
$7x-2x = 400$
$5x = 400$
$x = \frac{400}{5}$
$x = 80$
Therefore, the number of pages of the book $= 80$
Number of pages read $= \frac{1}{5} (80)+40 = 16+40 = 56$
Number of pages left to be read $= 80-56 = 24$.
Therefore, the Number of pages left to be read is 24.
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