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February $14$ is celebrated as International Book Giving Day and many countries in the world celebrate this day. Some people in India also started celebrating this day and donated the following number of books of various subjects to a public library :
History = $96$, Science = $240$, Mathematics = $336$.
These books have to be arranged in minimum number of stacks such that each stack contains books of only one subject and the number of books on each stack is the same.
Based on the above information, answer the following questions :
(i) How many books are arranged in each stack?
(ii) How many stacks are used to arrange all the Mathematics books?
(iii) (a) Determine the total number of stacks that will be used for arranging all the books.
OR
(iii) (b) If the thickness of each book of History, Science and Mathematics is $1.8$ cm, $2.2$ cm and $2.5$ cm respectively, then find the height of each stack of History, Science and Mathematics books.
History = $96$, Science = $240$, Mathematics = $336$.
These books have to be arranged in minimum number of stacks such that each stack contains books of only one subject and the number of books on each stack is the same.
Based on the above information, answer the following questions :
(i) How many books are arranged in each stack?
(ii) How many stacks are used to arrange all the Mathematics books?
(iii) (a) Determine the total number of stacks that will be used for arranging all the books.
OR
(iii) (b) If the thickness of each book of History, Science and Mathematics is $1.8$ cm, $2.2$ cm and $2.5$ cm respectively, then find the height of each stack of History, Science and Mathematics books.
Show SolutionHide Solution↓
(i) HCF $(96, 240, 336) = 48$
(ii) Number of stacks $= \frac{336}{48} = 7$
(iii) (a) Total number of stacks $= \frac{96}{48} + \frac{240}{48} + \frac{336}{48}$
$= 14$
OR
(b) Height of each stack of History $= 48 \times 1.8 = 86.4$ cm
Height of each stack of Science $= 48 \times 2.2 = 105.6$ cm
Height of each stack of Mathematics $= 48 \times 2.5 = 120$ cm
(ii) Number of stacks $= \frac{336}{48} = 7$
(iii) (a) Total number of stacks $= \frac{96}{48} + \frac{240}{48} + \frac{336}{48}$
$= 14$
OR
(b) Height of each stack of History $= 48 \times 1.8 = 86.4$ cm
Height of each stack of Science $= 48 \times 2.2 = 105.6$ cm
Height of each stack of Mathematics $= 48 \times 2.5 = 120$ cm