MATHEMATICS:
Case Study -1
LIBRARY
Aditya works as a librarian in Bright Children International School in Indore. He ordered for books on English, Hindi and Mathematics. He received 96 English books, 240 Hindi Books and 336 Math books. He wishes to arrange these books in stacks such that each stack consists of the books on only one subject and the number of books in each stack is the same. He also wishes to keep the number of stacks minimum.
Based on the above situation, answers the following questions:
(a) Find the number of books in each stack.
(b) Find the total number of stacks formed.
(c) How many stacks of mathematics books will be formed?
(d) If the thickness of each english book is 3 cm, then what will be the height of each stack of english books?
(e) If each hindi book weighs 1.5 kg, then find the weight of books in a stack of hindi books.
Answers
Answer:
the answer is attached in the form of pictures
Answer:
48 books in each stack.
Step-by-step explanation:
Given :- Number of English books = 96, Number of Hindi books = 240, Number of Mathematics book = 336. Each stack must have book of only one particular subject. Number of book in each stack must be same.
Solution :-
Number of English books = 96
Number of Hindi books = 240
Number of Mathematics book = 336
We need to find HCF of 96, 240, 336
96 = 2 ×2×2×2×2×3
240 = 2 ×2×2×2×3×5
336 = 2 ×2×2×2×3×7
∴ The HCF of 96, 240 and 336 is 48
So, there will be 48 books in each stack and there will be 2 stacks of English books, 5 stacks of Hindi books and 7 stacks of Mathematics books.
( a ) The number of books in each stack is 48
( b ) The total number of stacks formed = 2 + 5 + 7 = 14
( c ) Number of stacks of Mathematics books = 7
( d ) Thickness of each English book = 3 cm.
Height of each stack of English books = 3 × 48 = 144 cm.
( e ) Weight of each Hindi book = 1.5 kg.
Weight of books in a stack of Hindi books = 48 × 1.5 = 72 kg's.
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