Three sets of English,Hindi,and Mathematics b | vedclass

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Question

(A) Let $d$ be the number of books in each stack.Since all stacks must have the same height and books are of the same thickness,$d$ must be a common d

Vedclass · Accepted Answer

$2, 5, 7$

Vedclass · Answer

(A) Let $d$ be the number of books in each stack.Since all stacks must have the same height and books are of the same thickness,$d$ must be a common divisor of $96$,$240$,and $336$.To minimize the number of stacks,we need to maximize the number of books per stack,$d$. Thus,$d = 	ext{HCF}(96, 240, 336)$.Prime factorization:$96 = 2^5 	imes 3$$240 = 2^4 	imes 3 	imes 5$$336 = 2^4 	imes 3 	imes 7$$	ext{HCF}(96, 240, 336) = 2^4 	imes 3 = 16 	imes 3 = 48$.So,each stack contains $48$ books.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 $= \frac{336}{48} = 7$.Therefore,the number of stacks are $2, 5,$ and $7$ respectively.

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