Question

Ravish runs a book shop at school of math, gurgaon. He received 480 chemistry books,192 physics books and 672 mathmatics books of class XI. He whishes to average these books in minimum numbers of stacks such that each stack consists of the books on only one subject and the number of books in each stack is the same.
A)Find the number of books in each stack:
i) 26 ii)48 iii)24 iv)54
b) Number of stacks of mathematics books are:
i)24. ii)14 iii)60 iv)80
c) Minimum number of stacks of all the books are:
i)24 ii)25 iii)27 iv)28
d) Difference in number of stacks of mathematics books and sum of stacks of physics and chemistry books is
i)4 ii)10 iii)8 iv)0
e)If the thickness of each book of physics is 2.5cm then height of each stack is i)1.4m. ii)1.3m iii)1.2m iv)1m​

Answer 1

Solution :-

In order for minimum stacks Books in each stack must be maximum . So, we need to find the HCF of 480 , 192 and 672 .

So,

→ 480 = 2 * 2 * 2 * 2 * 2 * 3 * 5

→ 192 = 2 * 2 * 2 * 2 * 2 * 2 * 3

→ 672 = 2 * 2 * 2 * 2 * 2 * 3 * 7

then,

→ HCF = 2 * 2 * 2 * 2 * 2 * 3 = 96 (Ans. a)

therefore,

→ Number of stacks of mathematics books are = 672/96 = 7 (Ans.b)

→ Minimum number of stacks of all the books are = (480 + 192 + 672)/96 = 14 (Ans.c)

→ Difference in number of stacks of mathematics books and sum of stacks of physics and chemistry books is = 7 - (14 - 7) = 7 - 7 = 0 (Ans.d)

→ Height of each physics stacks = 2.5 * 96 = 240 cm = 2.4 m (Ans.e)\

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Answer 2

Average

Given:

Number of chemistry books is 480.

Number of physics books is 192.

Number of mathematics book is 672.

Number of books in each stack should be same.

Thickness of each physics book is 2.5 cm.

To find:

Minimum number of stacks such that each stack contains only one subject.

Number of books in each stack.

Number of stack of mathematics book.

Explanation:

Finding prime factors of all three numbers,

$480=2^{5}\times3\times5$

$192=2^{6} \times3$

$672=2^{5}\times3\times7$

H.C.F of these number is  $2^{5}\times3=96$

For minimum number of stacks such that each stack can contain books of same subject , there should be 96 books in a stack.

A) Number of books in each stack can be factor of 96, so from the option   it will be 24 or 48, but for minimum number of stack answer will be 48.

B) Number of stack of mathematics book = $\frac{672}{48}=14$ stacks.

C) Minimum number of stack of all books = $\frac{(480+192+672)}{48}=\frac{1344}{48}=28$stacks.

D) Difference in number of stacks of mathematics books and sum of stacks of physics and chemistry books is $\frac{672}{48} -(\frac{192}{48} +\frac{480}{48} ) = 0$

E) If the thickness of each book of physics is 2.5cm then height of each stack is $48\times2.5cm=120.0cm=1.2m$ , as $100cm=1m$.

A) (ii)

B) (ii)

C) (iv)

D) (iv)

E)  (iii)