Directions: Study the table carefully and answer the given question: | Publishing Houses | Number of Books Published | Ratio of Academic and Non-academic Books | Percentage of Books distributed | Number of distributors in publishing house | | :--- | :--- | :--- | :--- | :--- | | M | 28200 | 7 : 3 | 81 | 17 | | N | 32200 | 5 : 9 | 74 | 23 | | O | 29700 | 6 : 5 | 92 | 18 | | P | 31200 | 8 : 5 | 86 | 24 | | Q | 33800 | 7 : 6 | 79 | 25 | | R | 35700 | 11 : 6 | 82 | 21 | | S | 37800 | 5 : 13 | 89 | 24 | What is the average number of non-academic books published by publishers R and S?

### Concept & Weighted Averages Calculate the specific volume of non-academic books for both publishers using their respective ratios, then compute their arithmetic mean. $$ \text{Average} = \frac{\text{Value 1} + \text{Value 2}}{2} $$ ### Step-by-Step Solution 1. **Calculate Non-academic Books for R:** - Total Books = $35700$ - Ratio (Academic : Non-academic) = $11 : 6$. Total parts = $17$. - Non-academic = $35700 \times \left(\frac{6}{17}\right) = 2100 \times 6 = 12600$. 2. **Calculate Non-academic Books for S:** - Total Books = $37800$ - Ratio (Academic : Non-academic) = $5 : 13$. Total parts = $18$. - Non-academic = $37800 \times \left(\frac{13}{18}\right) = 2100 \times 13 = 27300$. 3. **Calculate the Average:** - $\text{Average} = \frac{12600 + 27300}{2} = \frac{39900}{2} = 19950$. ### Exam Strategy & Shortcut Notice the common factor when dividing by the ratio parts: $35700 / 17 = 2100$ and $37800 / 18 = 2100$. This makes calculation rapid. You can just sum the active ratio parts multiplied by this common factor: $\frac{(2100 \times 6) + (2100 \times 13)}{2} = \frac{2100 \times 19}{2} = 1050 \times 19 = 19950$. ### Common Pitfall Using the academic portion of the ratio instead of the non-academic portion. Always map the requested category to its correct ratio position (the second number in this case). ### Final Answer Therefore, the correct answer is **19950**.