too. The sets of English, Hindi and Mathematics books have to be stacked in such a
that all the books are stored topic wise and height of each stack is the same. The
number of English books is 96. the number of Hindi books is 240 and number of
mathematics books is 336, Assuming that the books are of the same thickness, the
number of stacks of English, Hindi and Mathematics books.
Answers
Answer:
The number of English, Hindi, and Math books is 96,240 and 336.
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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 the 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, determine the number of stacks of English, Hindi and Mathematics books.
Solution
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
H
C
F
Computation of
H
C
F
of
96
and
240
:
Clearly,
H
C
F
of
96
and
240
is
48
.
Computation of
H
C
F
of
48
and
336
:
Thus,
H
C
F
of
96
,
240
and
336
is
48
.
Hence, there must be
48
books in each stack.
Now, Number of stacks of English books
=
N
u
m
b
e
r
o
f
E
n
g
l
i
s
h
b
o
o
k
s
N
u
m
b
e
r
o
f
b
o
o
k
s
i
n
e
a
c
h
s
t
a
c
k
=
96
48
=
2
Number of stacks of Hindi books
=
N
u
m
b
e
r
o
f
H
i
n
d
i
b
o
o
k
s
N
u
m
b
e
r
o
f
b
o
o
k
s
i
n
e
a
c
h
s
t
a
c
k
=
240
48
=
5
and, Number of stacks of Mathematics books
=
N
u
m
b
e
r
o
f
M
a
t
h
e
m
a
t
i
c
s
b
o
o
k
s
N
o
.
o
f
b
o
o
k
s
i
n
e
a
c
h
s
t
a
c
k
=
336
48
=
7
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 Computation of 96, 240 and 336.
\begin{gathered}96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\ 240 = 2 \times 2 \times 2 \times 2 \times 3 \times 5 \\ 336 = 2 \times 2 \times 2 \times 2 \times 3 \times 7\end{gathered}
96=2×2×2×2×2×3
240=2×2×2×2×3×5
336=2×2×2×2×3×7
Therefore the HCF is 48.
Stacks of English books = 96/48 = 2
Stacks of Hindi books = 240/48 = 5
Stacks of Maths books = 336/48 = 7