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Home » 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?
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?
CBSE | Class 10 | Exercise 1B | Maths | Real Numbers | RS Aggarwal
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?

Answer:

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)

Using prime factorization:

336 = 24 × 3 × 7

240 = 24 × 3 × 5

96 = 25 × 3

HCF = 24 × 3

∴ HCF = 48

So, we made stacks of 48 books each.

∴ Number of stacks \begin{array}{l} = \frac{{336}}{{48}} + \frac{{240}}{{48}} + \frac{{96}}{{48}}\\ = 7 + 5 + 2\\ = 14 \end{array}

 

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