In a library 20% of the books are in Hindi, 50% of the remaining in English and 30% of the remaining are in French and rest 6300 books are in regional language. Then, find the number of books in the library?
Question
In a library 20% of the books are in Hindi, 50% of the remaining in English and 30% of the remaining are in French and rest 6300 books are in regional language. Then, find the number of books in the library?
Solution
Let's solve this step by step:
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Let's assume the total number of books in the library is X.
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According to the problem, 20% of the total books are in Hindi. So, the remaining books are 80% of X, which is 0.8X.
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50% of the remaining books (0.8X) are in English. So, the remaining books after removing the English ones are 50% of 0.8X, which is 0.5 * 0.8X = 0.4X.
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30% of the remaining books (0.4X) are in French. So, the remaining books after removing the French ones are 70% of 0.4X, which is 0.7 * 0.4X = 0.28X.
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According to the problem, the remaining books (0.28X) are 6300, which are in regional language.
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So, we can set up the equation 0.28X = 6300.
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To solve for X, we divide both sides of the equation by 0.28: X = 6300 / 0.28.
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After calculating the above expression, we find that X = 22500.
So, the total number of books in the library is 22500.
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