18.Three sets of Mathematics, physics and Biology books have to be
stacked in such a way that all the books are stored topic wise and the
height of each stack is same. The number of Mathematics books is 240,
the number of physics books is 960 and the number of Biology books
1024. Assuming that the books are of the same thickness, determine the
number of stack of each book. (Ans. 15, 60 and 64]
Answers
Answer:
Books of Mathematic in each set = 15
Books of Physic in each set = 60
Books of Biology in each set = 64.
Step-by-step explanation:
Since
By Prime factorization of numbers
240 = 2×2×2×2×3×5
960 = 2×2×2×2×2×3×5
1024 = 2×2×2×2×2×2×2×2×2×2
Now
We know that
Highest Common Factor = H.C.F = Common prime factors = 2×2×2×2 = 16
H.C.F = 16
So
we can able to make 16 sets of books of equal heights
And Thus books contain in each set are following
Books of Mathematic in each set = 240/16 = 15
Books of Physic in each set = 960/16 = 60
Books of Biology in each set = 1024/16 = 64.
So
Books of Mathematic in each set = 15
Books of Physic in each set = 60
Books of Biology in each set = 64.
Answer:
Three sets of physics chemistry and mathematics books have to be stacked.
Bur all the books are stored topic wise and the number of books in each stack is same.
Number of Physics books = 192
Number of Chemistry books = 240
Number of Mathematics books = 168
We will calculate the Highest Common Factor (HCF) of the numbers.
Factors of 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
Factors of 240 = 2 × 2 × 2 × 2 × 3 × 5
Factors of 168 = 2 × 2 × 2 × 3 × 7
Common factors = 2 × 2 × 2 × 3
HCF = 24
In each stack there are 24 books. Therefore, the number of stack of each subject would be
No. of stacks of Physics books = {192}{24}
= 8
No. of stacks of Chemistry books = {240}/{24}
= 10
No. of stacks of Mathematics books = {168}/{24}
= 7
The number of stacks of physics = 8, Chemistry = 10 and mathematics = 7