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 | How many books were given to each distributor by publisher Q if each publisher gets equal number of books?

### Concept & Averages First, find the total number of books distributed by calculating the given percentage of the total published books. Then, divide this amount evenly among the number of distributors. $$ \text{Books per Distributor} = \frac{\text{Total Distributed Books}}{\text{Number of Distributors}} $$ ### Step-by-Step Solution 1. **Find Total Books Distributed by Q:** - Total Published = $33800$ - Distribution Percentage = $79\%$ - Distributed Books = $33800 \times \left(\frac{79}{100}\right) = 338 \times 79$ - $338 \times 79 = 26702$ 2. **Divide Equally Among Distributors:** - Number of distributors in Q = $25$ - Books per distributor = $\frac{26702}{25} = 1068.08$ 3. **Analyze the Result:** - Since $1068.08$ is not an integer, the books cannot be distributed *perfectly* equally without a remainder. Therefore, none of the exact integer options accurately reflect an "equal" mathematical distribution. ### Exam Strategy & Shortcut To quickly multiply $338 \times 79$, use $338 \times (80 - 1) = 27040 - 338 = 26702$. Dividing by $25$ is the same as multiplying by $4$ and dividing by $100$: $26702 \times 4 = 106808 \rightarrow 1068.08$. Observing the decimal indicates that the integer option 1068 is technically incomplete. ### Common Pitfall Choosing option (b) 1068 by ignoring the decimal/remainder. In rigorous aptitude exams, if an exact division is implied ("equal number") and yields a decimal fraction for discrete objects like books, "None of these" is the mathematically correct choice. ### Final Answer Therefore, the correct answer is **None of these**.