# Math Help - percentage's

1. ## percentage's

Question: In a library 20% books are English, 50% of remaining are French and 30% of remaining are Latin. The rest 6300 are in regional languages. What's the total no. of books?

Answer: Let total books = x

Then no. of books in English= 20% of x= x/5
French = 2x/5
Latin = 3x/25

x-(x/5+2x/5+3x/25)=6300

Therefore x=22500

Another shortcut to solve this question using percentages is given as follows:

6300(100/100-20)(100/100-50)(100/100-30)= 22.500

I dont understand this shortcut. The Formulae that i've been given are:

To calculate % increase or decrease:

actual increase/original amount*100%

actual decrease/original amount*100%

If the price of something is increased by R%, then reduction in consumption so as not to increase the expenditure /OR/ If A is R% more then B, then B is less than A by:

[100*R/(100+R)]%

And the reverse of the above:

[100*(R/(100-R)]%

The part that i'm confused about in Shortcut solution is the application of the formulae.

IF "(100/100-20) (100/100-50) (100/100-30)" Is derived by applying one of the formula, then HOW has it been done? What is "100"?

Please Explain

Thank you

2. Originally Posted by Bish4n
Question: In a library 20% books are English, 50% of remaining are French and 30% of remaining are Latin. The rest 6300 are in regional languages. What's the total no. of books?

Answer: Let total books = x

Then no. of books in English= 20% of x= x/5
French = 2x/5
Latin = 3x/25

x-(x/5+2x/5+3x/25)=6300

Therefore x=22500

Another shortcut to solve this question using percentages is given as follows:

6300(100/100-20)(100/100-50)(100/100-30)= 22.500

I dont understand this shortcut.

...
If you want to calculate total number of books you have to calculate percentages of percentages:

Let x denote the total number of books then the number of non-English, non-French and non-Latin books can be calculated as:

$\underbrace{\underbrace{\underbrace{\left(x \cdot \frac{80}{100} \right)}_{non English\ books} \cdot \frac{50}{100}}_{nonFrench\ books} \cdot \frac{70}{100}}_{nonLatin\ books} = \underbrace{\underbrace{\underbrace{\left(x \cdot \frac{100-20}{100} \right)}_{nonEnglish\ books} \cdot \frac{100-50}{100}}_{nonFrench\ books} \cdot \frac{100-30}{100}}_{nonLatin\ books}=6300$

Now solve for x and you'll get the given formula.