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Three sets of English,Mathematics and Science …

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Three sets of English,Mathematics and Science books containing 336,240 and 96 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. How many stacks will be there?

Posted by Ayush Bharti 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Total number of English books = 336
Total number of mathematics books = 240
Total number of science books = 96
∴ Number of books stored in each stack = HCF (336, 240, 96)
Prime factorization:

{tex}\begin{array}{l}336=16\times21=2^4\times3\times7\\240=16\times15=2^4\times3\times5\\96=32\times3=2^5\times3\\So\;HCF(336,240,96)=2^4\times3=48\end{array}{/tex}

Hence, we make stacks of 48 books each

Number of stacks ={tex}\frac{336}{48}+\frac{240}{48}+\frac{96}{48}{/tex} = 7+5+2 = 14

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