Question

A boy read 2/7th of a book on the first day and 4/5th of the remainder on the another day. If there were 12 pages unread, how many pages did the book contains?

Answer 1

Answer:

84 pages

Step-by-step explanation:

To find :

Total pages of the book= ?

Solution :

Let the total pages of the book = $\italics{ \bold{x} }$

Pages read on 1st day = $\bold{\dfrac{2}{7} \ x}$

Pages read on 2nd day = $\bold{\dfrac{4}{5} \ of \ remaining \ pages}$

                                       = $\bold{\dfrac{4}{5} \ X \ (x- \frac{2}{7} x)}$

                                       = $\bold{\dfrac{4}{5} \ } \bold{x} \bold{\ (\frac{7x - 2x}{7})}$

                                       = $\bold{\dfrac{4}{5} \ } \bold{x} \bold{\ \dfrac{5x}{7}}$

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

Total pages read = $\bold{\dfrac{2}{7} \ x} + \bold{\dfrac{4}{7} \ x}$

                            = $\bold{\dfrac{6}{7} \ x}$  

⇒No. of unread pages = $\bold{x - \dfrac{6}{7} \ x}$

⇒                               12 = $\bold{\ (\dfrac{7x - 6x}{7})}$

⇒                               12 = $\bold{\ \dfrac{x}{7}}$

⇒                              x = 12 × 7

⇒                              x = 84 pages

∴  Total pages of the book = 84 pages