Three sets of English, Mathematics and Science books containing 336, 240 and 96 books respectively have to be stacked in such a way that all the books are stored subjectwise and the height of each stack is the same. Total number of stacks will be

### Concept & Logic When items of different quantities need to be grouped into equal, maximum-sized sets (ensuring same stack height), we find the Highest Common Factor (HCF). The total number of stacks is the sum of the stacks formed by each subject. ### Step-by-Step Solution * **Given:** Mathematics = 240 books, Science = 96 books, English = 336 books. * Calculate the HCF of 336, 240, and 96 to find the number of books in each single stack. * Find the prime factorization or common factors: $$336 = 12 \times 28$$ $$240 = 12 \times 20$$ $$96 = 12 \times 8$$ * We can see 4 is still common among 28, 20, and 8. $$336 = 48 \times 7$$ $$240 = 48 \times 5$$ $$96 = 48 \times 2$$ * So, the $\text{HCF} = 48$. This means there are 48 books in every stack. * Now, calculate the total number of stacks by dividing the number of books per subject by 48 and summing them. * Total stacks = $7 + 5 + 2 = 14$. ### Exam Strategy & Shortcut Don't do formal prime factorization. Notice that all numbers end in even digits and are clearly multiples of 12. Factor out 12 to get remaining quotients: $28, 20, 8$. The HCF of $28, 20, 8$ is $4$. The final quotients after factoring out $12 \times 4$ are $7, 5, 2$. Just add these final quotients: $7 + 5 + 2 = 14$ to get the total number of stacks directly. ### Common Pitfall The most common mistake is stopping calculation after finding the HCF (48) and choosing option (d). The question explicitly asks for the *total number of stacks*, not the number of books in each stack. Read the final sentence carefully! ### Final Answer **Therefore, the correct answer is 14.**