Question

Three sets of English Mathematics and Science books containing $336,240and96$ 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. $48$

Answer 1

The correct option is A $14$

Height of each stack = HCF of (336, 240, 96) books
$\therefore 336=2^4\times 3\times 7$ $\Rightarrow HCF=2^4\times 3=48$
$\therefore 240=2^4\times 3\times 5$ $\Rightarrow HCF=2^4\times 3=48$
$\therefore 96=2^5\times 3$ $\Rightarrow HCF=2^4\times 3=48$
Height of each stack = 48 books
$\Rightarrow$ Number of stack = $\frac{336}{48}+\frac{240}{48}+\frac{96}{48}$
=7 + 5 + 2 = 14