A boy read 3/4 th of the book on one day and 4/5th of the remainder on aonther day. If there were 30 pages unread: How many pages did contain ?

And the three fourth of the book is 3/4 of x = 3x/4

He read 3/4

^{th}of the book, so the pages left = x- 3x/4 = x/4

So the remainder = x/4

He read 4/5

^{th}

^{ }of the remainder on the next day so 4/5

^{th}

^{ }of x/4 = x/5

Since 30 pages are unread

so we have

x-(3x/4) - (x/5) = 30

$\frac{x}{1}-\frac{3x}{4}-\frac{x}{5}=30\phantom{\rule{0ex}{0ex}}ortakingLCMof4,5,1weget20,so\phantom{\rule{0ex}{0ex}}\frac{20x-15x-4x}{20}=30\phantom{\rule{0ex}{0ex}}\frac{x}{20}=30\phantom{\rule{0ex}{0ex}}x=600\phantom{\rule{0ex}{0ex}}Sothenumberofpagesis600pages.$

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