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In a library 5 percent books are in English, 10 percent of the remaining are in hindi and 15 percent of the remaining are in Sanskrit. The remaining 11628 books are in French. Then find the total number of books in the library.
- a)8000
- b)12000
- c)16000
- d)20000
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a library 5 percent books are in English, 10 percent of the remaini...
5% of books are in English,
10% of remaining books are in Hindi,
15% of remaining books are in Sanskrit.
Remaining books are in french = 11628
Calculation:
Let the total books in the library be 100%
According to question:
5% of books are in English
Remaining books = 100 - 5 = 95%
10% of remaining are in hindi = 10% of 95 = 9.5
Remaining books = 95 - 9.5 = 85.5%
15% of remaining books are in sanskrit = 15% of 85.5 = 12.825%
Remaining books = 85% - 12.825% = 72.675%
According to question:
72.675% = 11628
⇒ 1% = (11628/72.675)
⇒ 100% = (11628/72.675)× 100 = 16000
∴ Required value = 16000
Most Upvoted Answer
In a library 5 percent books are in English, 10 percent of the remaini...
Given information:
- 5% of the books are in English
- 10% of the remaining books are in Hindi
- 15% of the remaining books are in Sanskrit
- 11628 books are in French
To find:
The total number of books in the library
Solution:
Let the total number of books in the library be x.
Books in English = 5% of x = 0.05x
Remaining books = x - 0.05x = 0.95x
Books in Hindi = 10% of (remaining books) = 0.10(0.95x) = 0.095x
Remaining books = 0.95x - 0.095x = 0.855x
Books in Sanskrit = 15% of (remaining books) = 0.15(0.855x) = 0.12825x
Remaining books = 0.855x - 0.12825x = 0.72675x
Books in French = 11628
Therefore, we have the equation:
0.05x + 0.095x + 0.12825x + 11628 = x
0.27325x = 11628
x = 42534.71
Since the number of books must be a whole number, we round up to the nearest integer:
x = 42535
Hence, the total number of books in the library is 42535, which is closest to option (c) 16000.
- 5% of the books are in English
- 10% of the remaining books are in Hindi
- 15% of the remaining books are in Sanskrit
- 11628 books are in French
To find:
The total number of books in the library
Solution:
Let the total number of books in the library be x.
Books in English = 5% of x = 0.05x
Remaining books = x - 0.05x = 0.95x
Books in Hindi = 10% of (remaining books) = 0.10(0.95x) = 0.095x
Remaining books = 0.95x - 0.095x = 0.855x
Books in Sanskrit = 15% of (remaining books) = 0.15(0.855x) = 0.12825x
Remaining books = 0.855x - 0.12825x = 0.72675x
Books in French = 11628
Therefore, we have the equation:
0.05x + 0.095x + 0.12825x + 11628 = x
0.27325x = 11628
x = 42534.71
Since the number of books must be a whole number, we round up to the nearest integer:
x = 42535
Hence, the total number of books in the library is 42535, which is closest to option (c) 16000.
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Community Answer
In a library 5 percent books are in English, 10 percent of the remaini...
DETAILED SOLUTION
let total no. of books be X
5%of X = X/20,no.of books in hindi
X-20/X=19X/20remaining books excluding books in hindi
19X/20×10/100=19X/200 no. of books in English
3rd step X-X/20+19X/200=171X/200no. of books excluding hindi and English books
171X/200×15/100=513X/4000 no.of books in sanskrit
X-X/20+19X/200+513X/4000=2907X/4000no. of books in French
2907X=11628×4000
=16000 total no. of books
let total no. of books be X
5%of X = X/20,no.of books in hindi
X-20/X=19X/20remaining books excluding books in hindi
19X/20×10/100=19X/200 no. of books in English
3rd step X-X/20+19X/200=171X/200no. of books excluding hindi and English books
171X/200×15/100=513X/4000 no.of books in sanskrit
X-X/20+19X/200+513X/4000=2907X/4000no. of books in French
2907X=11628×4000
=16000 total no. of books
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