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 Ilindi books is 240 and the number of Mathematics books is 336.
Assuming that the books are of same thickness, determine the number of stacks of English,
Hindi and Mathematics books.
urgent hai plz answer fast​

Answer 1

$\large\underline{\sf{Solution-}}$

➢ Given that, there are

Three sets of English, Hindi and Mathematics books of 96, 240 and 336 respectively.

Need to be stacked in such a way that all the books are stored topic wise and the height of each stack is the same

➢ It means, we have to find the largest number which divides 96, 240 and 336 exactly.

And, we know that

➢ That number is HCF ( 96, 240, 336 ).

CONSIDER,

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 96}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:96 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:48 \:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:24\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:12 \:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:6\:\:}}\\\underline{\sf{3}}&\underline{\sf{\:\:3\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 96 = {2}^{5} \times 3}$

CONSIDER

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 240}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:240 \:\:}}}\\\underline{\sf{2}}&\underline{\sf{\:\:120\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:60 \:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:30\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:15 \:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\:\:5\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 240 = {2}^{4} \times 3 \times 5}$

CONSIDER :-

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 336}$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:336 \:\:}}}\\\underline{\sf{2}}&\underline{\sf{\:\:168\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:84 \:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:42\:\:}} \\ {\underline{\sf{3}}}& \underline{\sf{\:\:21 \:\:}} \\ {\underline{\sf{7}}}& \underline{\sf{\:\:7\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 336 = {2}^{4} \times 3 \times 7}$

Thus, we have now

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 96 = {2}^{5} \times 3}$

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 240 = {2}^{4} \times 3 \times 5}$

$\red{\rm :\longmapsto\:Prime \: Factorization \: of \: 336 = {2}^{4} \times 3 \times 7}$

$\green{\bf\implies \:HCF(96,240,336) = {2}^{4} \times 3 = 48}$

Hence,

There must be 48 books in each stack.

Now,

$\blue{\rm :\longmapsto\:Number \: of \: stacks \: of \: english \: book = \dfrac{96}{48} = 2}$

$\blue{\rm :\longmapsto\:Number \: of \: stacks \: of \: hindi \: book = \dfrac{240}{48} = 5}$

$\blue{\rm :\longmapsto\:Number \: of \: stacks \: of \: mathematics \: book = \dfrac{336}{48} = 7}$

Additional Information :-

Practice problem of same type. Try yourself !!

Question :- 1 In a seminar, the number of participants in Hindi, English ane Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

Answer :- 10

Question :- 2 https://brainly.in/question/41489044