Percentages
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Q.

In a library, $20\%$ of the books are in Hindi. $50\%$ of the remaining are in English and $30\%$ of the remaining are in French. The remaining $6,300$ books are in regional languages.

What is the total number of books in library?

 A.

19,500

 B.

20,500

 C.

21,500

 D.

22,500

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Solution:
Option(D) is correct

Let the total number of books in the library be $x$.

$20\%$ of these books are in Hindi $= 0.2x$ books in Hindi.

Therefore the remaining books $= x - 0.2x = 0.8x$ books.

$50\%$ of these remaining books are in English $= 50\% \text{ of } 0.8x = 0.4x$ books.

Therefore the remaining books $= 0.8x - 0.4x = 0.4x$ books.

$30\%$ of these remaining books are in French $= 30\% \text{ of } 0.4x = 0.12x$ books.

Now the remaining books $= 0.4x - 0.12x = 0.28x$ books.

According to the question the total remaining books $= 6300$.

$\Rightarrow 0.28x=6300$

$\Rightarrow x = \dfrac{6300}{0.28}$

$\Rightarrow x = 22,500 \text{ books.}$

Hence, the total number of books in the library $= \textbf{22,500 books.}$


(1) Comment(s)


Zoha Amjad
 ()

total books * 80% * 50% * 70% = 6300

total books = 22500