Question

plz tell this question pls

Answer 1

Answer:

The number of stacks in each topic are:

English:   2

Hindi:   5

Sociology:   7

Hope this helps you.

Step-by-step explanation:

Let n be the number of books in each stack ( all stacks are the same size ).

Let e be the number of stacks of English, let h be the number of stacks of Hindi, and let s be the number of stacks of Sociology.

Then

ne = 96,  nh = 240  and  ns = 336.

This shows that n is a common divisor of 96, 240 and 336.

The prime factorizations of these numbers are:

96 = 2⁵ × 3¹

240 = 2⁴ × 3¹ × 5¹

336 = 2⁴ × 3¹ × 7¹

The problem doesn't actually say that the stacks should be as large as possible, so in principle, we would use any common divisor.  However, they probably meant for us to make the stacks as large as possible, so for n we take the greatest common divisor (or highest common factor).  From the prime factorizations, this is seen to be:

n = 2⁴ × 3¹ = 48

So the stacks are each 48 books high.

The number of stacks in each topic are:

English:  e = 96 / n = 96 / 48 = 2

Hindi:  h = 240 / n = 240 / 48 = 5

Sociology:  s = 336 / n = 336 / 48 = 7