Question

Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same. The number of English books is $96,$ the number of Hindi books is $240$ and the number of Mathematics books is $336.$ Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

Answer 1

In order to arrange the books as required, we have to find the largest number that divides $96,240$ and $336$ exactly. Clearly, such a number is their $HCF$ Computation of $HCF$ of $96$ and $240$:
Clearly, $HCF$ of $96$ and $240$ is $48$.
Computation of $HCF$ of $48$ and $336$:
Thus, $HCF$ of $96,240$ and $336$ is $48$.
Hence, there must be $48$ books in each stack.
Now, Number of stacks of English books $=\frac{NumberofEnglishbooks}{Numberofbooksineachstack}=\frac{96}{48}=2$
Number of stacks of Hindi books $=\frac{NumberofHindibooks}{Numberofbooksineachstack}$ $=\frac{240}{48}=5$
and, Number of stacks of Mathematics books $=\frac{NumberofMathematicsbooks}{No.ofbooksineachstack}=\frac{336}{48}=7$