CM of
4. Ravish runs a book shop at school of M
Gurgaon, He received 480
chemistry be
192 physics books and 672 Mathema
books of class XI.
5360
5360
roduct
5
*3!
*3!
He whishes to average these book
minimum numbers of stacks such thatd
stack consists of the books on only
subject and the number of books in
stack is the same
being
f your
tree.
your
ience
and
(a) Find the number of books in e
stack
(i) 26
(1) 48
(in) 24
(b) Number of stacks of Mathema
(iv) 54
15
books are
29
(1) 24
(iii) 60
(C) Minimum number of stacks of
(ii) 14
(iv) 80
gasil
y
the books are
(1) 24
(iii) 27
(d) Difference in number of sta
of Mathematics books and sum
(11) 25
th) 28
om
2
stacks of Physics and Chemie
books is
(i) 10
(ivo
18
(e) If the thickness of each book
physics is 2.5 cm then height of
stack is
0 1 4 m
(in 1.2 m
(h) Ima
Answers
Answer:
Rs. 20,160
No. of chemistry books =10 dozen =10×12=120
No. of physics books =8 dozen =8×12=96
No. of Economics books =10 dozen =10×12=120
Now, S.P of 1 chemistry book = Rs. 80
S.P of 1 Physics book = Rs. 60
S.P. of 1 economic book = Rs. 40
Total S.P. =[
120
96
120
]
⎣
⎢
⎢
⎡
80
60
40
⎦
⎥
⎥
⎤
=120×80+96×60+120×40
=9600+5760+4800
= Rs. 20160
- a) The number of books in each stack = 96 .
- b) Number of stacks of mathematics books = 7
- c) Minimum number of stacks of all the books = 14
- d) Difference in number of stacks of mathematics books and sum of stacks of physics and chemistry books = 0
- e) If the thickness of each book of physics is 2.5cm then height of each stack is = 2.4 m .
Given :-
- Total chemistry books = 480
- Total physics books = 192
- Total mathematics books = 672
To Find :-
a) The number of books in each stack ?
b) Number of stacks of mathematics books ?
c) Minimum number of stacks of all the books ?
d) Difference in number of stacks of mathematics books and sum of stacks of physics and chemistry books ?
e) If the thickness of each book of physics is 2.5cm then height of each stack is ?
Solution :-
In order to find minimum number of stacks , books in each stack must be maximum .
So,
→ Number of books in each stack = HCF of 480, 192, 672
Then, finding the HCF of 480 , 192 and 672 by prime factorization method we get,
→ 480 = 2 * 2 * 2 * 2 * 2 * 3 * 5
→ 192 = 2 * 2 * 2 * 2 * 2 * 2 * 3
→ 672 = 2 * 2 * 2 * 2 * 2 * 3 * 7
So,
→ HCF = 2 * 2 * 2 * 2 * 2 * 3 = 96 (a)
therefore, we can conclude that, the number of books in each stack are 96 .
Now,
→ Number of stacks of chemistry books = 480/96 = 5
→ Number of stacks of physics books = 192/96 = 2
→ Number of stacks of mathematics books = 672/96 = 7 (b)
and,
→ Minimum number of stacks of all the books are = Total number of books / Books in each stack = (480 + 192 + 672)/96 = 1344/96 = 14 (c)
also,
→ Difference in number of stacks of mathematics books and sum of stacks of physics and chemistry books is = 7 - (5 + 2) = 7 - 7 = 0 (d)
and,
→ Height of physics book stack = Height of each physics books × Total books in stack = 2.5 * 96 = 240 cm = 2.4 m (e)
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