Question

A school has a book bank for the help of students from economically weaker section.

Students of class X donated the following number of books to the book bank.

English - 96, Hindi - 240, Mathematics – 336

These books have to be stacked in such a way that all the books are stored topic

wise and number of copies in each stack are same. Based on the above situation,

answer the following questions.

i) To find the maximum number of books in each stack, we need to calculate

____________ of numbers.

a) HCF b) LCM c) product d) sum. ii) Maximum number of books in each stack is __________.

a) 48 b) 3360 c) 1680 d) 672

iii) Prime factorization of 336 is ___________.

a) 2

5 × 7 b) 2

4 × 3 × 7 c) 2

5 × 3 d) 2

5 × 3 × 7

iv) The decimal expansion of the rational number formed by taking number of

Hindi books as numerator and number of Mathematics books as denominator

is ___________.

a) terminating b) non-terminating repeating

c) non-terminating non-repeating d) none of these​

Answer 1

1 non terminating 2non repeating

Answer 2

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.

We have,

96=2

5

×3,240=2

4

×3×5 and 336=2

4

×3×7

∴ HCF of 96,240 and 336 is 2

4

×3=48

So, there must be 48 books in each stack.

∴ Number of stacks of English books=

48

96

=2

Numberof stacks of Hindi books=

48

240

=5

Number of stacks of Mathematics books=

48

336

=7