Question

10. A boy read 3/4 of the book on Monday and 4/5 of the remainder on Tuesday. If there were 30 pages unread, how
many pages did the book contain?​

Answer 1

A boy read 3/4 of pages on Monday,

4/5 of the remaining pages on Tuesday,

Carefully observe that he gave he read 4/5 of remainder pages on Tuesday ; which means that 1/5 is left of the remaining pages, that 1/5 is 30 pages.

So , the 4/5 of remaining  pages are = 30 x4 = 120 pages,

and the total remaining are = 5/5 = 30 x 5 = 150 pages are the remaining pages.

And first, he gave that he read 3/4 of the book, which means that  the remaining 1/4 = 120 pages ;

then the 3/4 pages  = 3 x 120

So, The pages he read on Monday = 360 pages ;

So the total pages = 360[ Monday ] + 120[Tuesday + remaining pages] pages ;

Total pages = 480 pages

So the book has 480 pages in total.

Answer 2

Concept: This is a simple word problem based on a linear equation. It contains operations on fractions and simple calculations. In this type of question first, we assume the unknown quantity and then follow the given statement in question.

Given:  A boy read 3/4 of the book on Monday and 4/5 of the remainder on Tuesday. There were 30 pages of unread

To find: How many pages did the book contain?

Solution:

Let the book contains 'x' pages

According to the statement of the question,

$\frac{3}{4}$ of the read on Monday= $\frac{3}{4}x$

$\frac{4}{5}$ of the remainder on Tuesday= $\frac{4}{5}$($x-\frac{3}{4}x$)

If there were 30 pages unread in the book, then how many pages book have?

    $x-$${$[$\frac{3}{4}x+\frac{4}{5} (x-{\frac{3}{4}x)$]=$30$

⇒ $x-[\frac{3}{4}x + \frac{4}{5} (\frac{x}{4})]=30$

⇒ $x-[\frac{3}{4}x+\frac{x}{5}]=30$

⇒ $x-\frac{19}{20} x$$= 30$

⇒ $\frac{1}{20}x=30$

⇒ $x=600$

Hence the book contains 600 pages