There are some history books and some geography books in a library. The books…
2025
There are some history books and some geography books in a library. The books that 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.
- A.
2:3
- B.
5:2
- C.
4:3
- D.
5:7
Attempted by 35 students.
Show answer & explanation
Correct answer: A
Solution: Use a weighted average to find the ratio of history to geography books.
Let the number of history books be H and the number of geography books be G.
The overall average pages read gives the equation (164H + 154G)/(H + G) = 158.
Multiply both sides and rearrange: 164H + 154G = 158H + 158G ⇒ 164H − 158H = 158G − 154G ⇒ 6H = 4G.
Thus H/G = 4/6 = 2/3, so the ratio of history to geography books is 2:3.
Verification: With H = 2 and G = 3, average = (164*2 + 154*3)/5 = (328 + 462)/5 = 790/5 = 158.
Answer: 2:3