Question

There are some history books and some geography books in a library. The books that were read were read cover to cover. The average number of pages read for all these books is 158. If the average number of pages read for history books is 164 and that for geography books is 154, find the ratio of no. of history books to that of geography books?

Answer 1

Answer:

The ratio of no. of history books to that of geography books is 2 : 3

Step-by-step explanation:

Let the number of history books be x and the number of geography books be y

Average no. of pages in history books = 164

Total pages in history books = 164x

Average no. of pages in geography books = 154

Total pages in geography books = 154y

Total pages both in history and geography books combined

= 164x + 154y

Average number of pages both in history and geography books combined

= (164x + 154y)/(x+y)

According to the question

$\frac{164x + 154y}{x+y} =158$

$\implies 164x + 154y} =158x+158y$

$\implies 6x =4y$

$\implies \frac{x}{y} =\frac{4}{6} =\frac{2}{3}$

or, $\implies x:y=2:3$

Hope this helps.