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 $HCF$.

We have,

$96=2\times 2\times 2\times 2\times 2\times 2\times 3$

$240=2\times \times 2\times 2\times 2\times 3\times 5$

and, $336=2\times \times 2\times 2\times 2\times 3\times 7$

$\therefore HCF$ of $96,240$ and $336$ = $2\times \times 2\times 2\times 2\times 3=48$

So, there must be $48$ books in each stack.

$\therefore$ Number of stacks of English books$=\frac{96}{48}=2$

Number of stacks of Hindi books$=\frac{240}{48}=5$

Number of stacks of Mathematics books$=\frac{336}{48}=7$