Question

MATHEMATICS:

Case Study -1

LIBRARY

Aditya works as a librarian in Bright

Children International School in Indore. He

ordered for books on English, Hindi and

Mathematics. He received 96 English

books, 240 Hindi Books and 336 Math

books. He wishes to arrange these books

in stacks such that each stack consists of

the books on only one subject and the

number of books in each stack is the

same. He also wishes to keep the number

of stacks minimum.

Based on the above situation, answers the following questions:

(a) Find the number of books in each stack.

(b) Find the total number of stacks formed.

(c) How many stacks of mathematics books will be formed?

(d) If the thickness of each english book is 3 cm, then what will be the height of each stack of english

books?

(e) If each hindi book weighs 1.5 kg, then find the weight of books in a stack of hindi books.​

Answer 1

Given :

Number of English books received by aditya = 96

Number of Hindi books received by aditya = 240

Number of Maths books received by aditya = 336

Thickness of english book = 3 cm

Weight of hindi book = 1.5 kg

To Find :

a. The number of books in each stack.

b. The total number of stacks formed.

c. The number of stacks of mathematics book.

d. The height of each stack of english.

e. The weight of books in a stack of hindi books.

Solution :

We need to find the highest common factor of 96, 240, 336 .

The prime factorization of 96, 240, 336 :

$96 \: = 2 {}^{5 } \times 3$

$240 \: = 2 {}^{4} \times 3 \times 5$

$336 \: = 2 {}^{4} \times 3 \times 7$

The required HCF of 96, 240, 336

$= \: 2 {}^{4} \times 3$

$= 16 \times 3 = 48$

a. The number of books in each stack = 48 .

The total number of books = 96 + 240 + 336 = 672

Number of books in each stack = 48

b. The total number of stacks formed = 672/48

= 14

c. Number of stacks of mathematics books formed

= 336/48

= 7

Number of books in each stack of english books = 48

Thickness of each english book = 3 cm

d. Height of each stack of english books = 48 × 3

= 144 cm

Weight of each hindi book = 1.5 kg

e. The weight of books in a stack of hindi books

= 1.5 × 48

= 72 kg