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Q.

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?


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a

12

b

14

c

16

d

20 

answer is B.

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Detailed Solution

Given is three sets of English, Mathematics and Science books containing 336, 240 and 96 books respectively. We have to find the number of stacks with same heights in which 336 English books, 240 Mathematics books and 96 Science books can be arranged.
So, the total number of books in a stack will be the HCF of 336, 240 and 96.
Now, we will proceed with the prime factorization of 336, 240 and 96 as follows,
336= 2 4 ×3×7 240= 2 4 ×3×5 96= 2 5 ×3
So, we have,
HCF (336, 240, 96)
= 2 4 ×3=48
So, there are 48 books present in each stack.
Therefore, the number of stacks of books of each subject will be
= 336+240+96 48 = 672 48 =14
Thus, there are 14 stacks of equal height.
Hence, the correct option is (2).
 
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