question_answer

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 subject wise and the height of each stack is the same. Total number of stacks will be

A) 14

B) 21

C) 22

D) 48

Correct Answer: A

Solution :

[a] Factors of \[336={{2}^{4}}\times 3\times 7\] Factors of \[240={{2}^{4}}\times 3\times 5\] Factors of \[96={{2}^{5}}\times 3\] HCF \[=(24\times 3)=48\] So, we make stacks of 48 books each. Number of stacks \[=\left( \frac{336}{48}+\frac{240}{48}+\frac{96}{48} \right)\] \[=(7+5+2)=14\]