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A library contained books in Hindi, English and several regional languages, such that the average number of books per language are 525, while the average number of books per regional language are 225. If the total number of Hindi and English books in the library is 2100 more than the total number of books in the regional languages, find the number of regional languages in which books are kept in the library.

A library contained books in Hindi, English and several regional languages, such that the average number of books per language are 525, while the average number of books per regional language are 225. If the total number of Hindi and English books in the library is 2100 more than the total number of books in the regional languages, find the number of regional languages in which books are kept in the library. Correct Answer 14

Let the number of regional languages be ‘x’

⇒ Total no. of languages = x + 2

∵ Average no. of books per language = 525

⇒ Total no. of books in library = 525 × (x + 2) = 525x + 1050

Also, average no. of books per regional language = 225

⇒ Total no. of books in regional languages = 225x

⇒ Total no. of books in Hindi and English = 525x + 1050 – 225x = 300x + 1050

Now,

Total no. of books in Hindi and English – Total no. of books in regional languages = 2100

⇒ 300x + 1050 – 225x = 2100

⇒ x = 1050/75 = 14

∴ No. of regional languages = 14

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