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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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