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 | If the total number of books published by publishers P, Q and R is increased by 30% and the total number of books published by remaining publishers be decreased by 20%, what will be the new average of books published by all the publishers?

### Concept & Percentage Alterations Apply the distinct percentage increase and decrease to the designated groups of publishers, sum the newly generated totals, and divide by the total number of publishers ($7$) to find the new average. $$ \text{New Average} = \frac{\text{New Total Sum}}{\text{Total Number of Entities}} $$ ### Step-by-Step Solution 1. **Group 1: P, Q, and R (Increased by $30\%$)** - Original Sum = $31200 + 33800 + 35700 = 100700$ - New Sum = $100700 \times 1.30 = 130910$ 2. **Group 2: M, N, O, and S (Decreased by $20\%$)** - Original Sum = $28200 + 32200 + 29700 + 37800 = 127900$ - New Sum = $127900 \times 0.80 = 102320$ 3. **Calculate New Overall Average:** - New Total Books = $130910 + 102320 = 233230$ - Total Publishers = $7$ - $\text{New Average} = \frac{233230}{7} = 33318.5714...$ ### Exam Strategy & Shortcut When dividing $233230$ by $7$, observe the calculation: $233 / 7 = 33$ with a remainder of $2$. $22 / 7 = 3$ with remainder $1$. $13 / 7 = 1$ with remainder $6$. $60 / 7 = 8$ with remainder $4$. The result is $33318$ with a fractional remainder ($4/7$). Because $33318$ is provided as option (b) but is not the exact mathematical answer, marking "None of these" is the precise choice for decimal non-matches. ### Common Pitfall Accidentally omitting a publisher when summing the "remaining publishers", or incorrectly calculating the new average by simply averaging the averages of the two separate groups. ### Final Answer Therefore, the correct answer is **None of these**.