1. 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 same. The number of English books is 96,the
number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are
of the same thickness. Using this data answer the following questions
i. The maximum number of books in each stack is
a) 12 b) 24 c) 48 d) 36
ii. Number of stacks of English books is
a) 2 b) 7 c) 5 d) 12
iii. Number of stacks of Mathematics books is
a) 2 b) 7 c) 5 d) 12
iv. Number of stacks of Hindi books is
a) 2 b) 7 c) 5 d) 12
v. Which Mathematical concept was used in finding the maximum number of books in each stack?
a) LCM b) HCF c) Neither HCF nor LCM d) Fundamental theorem of Arithmetic
Answers
Answer:
In order to arrange the books as required, we have to find the largest number that divides 96,240 and 336 exactly. Clearly, such a number is their HCF.
We have,
96=2
5
×3,240=2
4
×3×5 and 336=2
4
×3×7
∴ HCF of 96,240 and 336 is 2
4
×3=48
So, there must be 48 books in each stack.
∴ Number of stacks of English books=
48
96
=2
Numberof stacks of Hindi books=
48
240
=5
Number of stacks of Mathematics books=
48
336
=7
Step-by-step explanation:
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Given : 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 same
The number of English books is 96
The number of Hindi books is 240
The number of Mathematics books is 336
To Find : The maximum number of books in each stack
Number of stacks of English books
Number of stacks of Mathematics books
Number of stacks of Hindi books
Mathematical concept used in finding the maximum number of books in each stack
Solution :
To find maximum number of books in each stack need to find HCF of books of each subject.
HCF (96 , 240 , 336)
HCF Highest common factor of given numbers is the largest factors which divides all the given numbers perfectly.
HCF = product of common factors of least power
96 = 2 * 2 * 2 * 2 * 2 * 3
240 = 2 * 2 * 2 * 2 * 3 * 5
336 = 2 * 2 * 2 * 2 * 3 * 7
HCF = 2 * 2 * 2 * 2 * 3 = 48
i. The maximum number of books in each stack is a) 48
ii. Number of stacks of English books = 96/48 = 2
correct option is a) 2
iii. Number of stacks of Mathematics books is = 336/48 = 7
correct option is b) 7
iv. Number of stacks of Hindi books is = 240/48 = 5
correct option is c) 5
Mathematical concept used in finding the maximum number of books in each stack is HCF
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