The sets of Physics, Chemistry 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 Physics books is 12, the number of Chemistry books 20 and the number of Mathematics books is 30. Assuming that the books are of the same thickness, determine the number of stacks of Physics, Chemistry and Mathematics books.
In order to arrange the books as required, we have to find the largest number that divides 12, 20 and30 exactly. Clearly, we have to find HCF. Now,
Since, 12 = 2 × 2 × 3 = 22 × 3
20 = 2 × 2 × 5 = 22 × 5
and 30 = 2 × 3 × 5
HCF = Product of common prime factors with lowest powers
= 2
So, there must be 2 books in each stack.
∴ Number of stacks of Physics books
Number of stacks of Chemistry books
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Number of stacks of Mathematics books
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