The average number of pages of nine book is 400. If the average number of pages of the first five books is 430 and that of last five books is 380, then what is the number of pages of the fifth book?

The average number of pages of nine book is 400.

total number of pages of nine books = $$400\times\ 9$$ = 3600    Eq.(i)

If the average number of pages of the first five books is 430.

total number of pages of five books = $$430\times\ 5$$ = 2150    Eq.(ii)

the average number of pages of the last five books is 380.

total number of pages of five books = $$380\times\ 5$$ = 1900    Eq.(iii)

number of pages of the fifth book =  Eq.(ii)+ Eq.(iii)-Eq.(i)

= 2150+1900-3600

= 4050-3600

= 450