Question

A man reads 3/7 of a book on a day and 2/5 of the remaining, on the second day. If the number of pages still unread are 36, how many pages did the book contain ?

A) 105 B) 101 C) 98 D) 109

Answer 1

Given ,

Fraction of book read in 1st day = 3/7

Fraction read of remaining = 2/5

Pages left unread = 36

To Find :-

Total no. of pages in the book

Solution :-

Let the total no. of pages be x

Pages read in 1st day = 3/7 of x

$=\: {\dfrac{3 \times x}{7}}$

$=\: {\dfrac{3x}{7}}$

Pages left for reading

$=\: x\: -\: {\dfrac{3x}{7}}$

$=\: {\dfrac{7x - 3x}{7}}$

$=\: {\dfrac{4x}{7}}$

Pages read on second day

$=\: {\dfrac{2}{5}} \times {\dfrac{4x}{7}}$

$=\: {\dfrac{8x}{35}}$

Total no. of pages left = 36

According to question,

${\dfrac{3x}{7}}\: +\: {\dfrac{8x}{35}}\: +\: 36\: =\: x$

LCM of 7 & 35 is 35

${\dfrac{15x\: +\: 8x}{35}}\: +\: 36\: =\: x$

${\dfrac{23x}{35}}\: +\: 36\: =\: x$

$x\: -\: {\dfrac{23x}{35}}\: =\: 36$

${\dfrac{35x - 23x}{35}}\: =\: 36$

${\dfrac{12x}{35}}\: =\: 36$

$x\: =\: {\dfrac{36 \times 35}{12}}$

x = 105

Therefore, total number of pages in the book is 105