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A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4th of the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?
  • a)
    60
  • b)
    110
  • c)
    130
  • d)
    140
  • e)
    190
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A school library consists of literature books and science books in the...
Given:
  • Let the number of literature books be l and the number of science books be s
    • l : s = 5 : 6
  • Number of literature books added = 50
    • Total literature books now = l + 50
  • Number of science books increased = ¼ * s
    • Total science books now = s + ¼ * s
  • New Ratio of literature and science books = 4 : 3
To Find: Initial number of books in the library
  • Value of l + s?
Approach:
  1. To Find the value of l + s, we need to find the values of l and s.
  2. We know that l : s = 5 : 6. So, we need to find another relation between l and s to find unique values of l and s.
  3. We are given that the new number of literature books = l + 50 and the new number of science books is s + ¼ * s. The ratio of these literature and science books is 4 : 3
    • So, we have here another relation between l and s
Working out:
a. So, we have 3l + 150 = 5s, i.e. 5s – 3l = 150…….(2)
3. Adding equations (1) and (2), we have 3l = 150, i.e. l = 50
a. Putting the value of l in equation (2), we have 5s = 150 + 150, i.e. s = 60
4. Hence, initial books in the library = l + s = 50 + 60 = 110
Thus, the library initially had 110 books in total.
Answer : B
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Most Upvoted Answer
A school library consists of literature books and science books in the...
Given:
Ratio of literature books to science books = 5:6
Let the common factor be x. So, the number of literature books will be 5x and the number of science books will be 6x.

50 more literature books are added to the library, so the new number of literature books = 5x + 50
Also, the number of science books is increased by 1/4th of the existing science books, so the new number of science books = 6x + 6x/4 = 9x/2

The ratio of literature books to science books after the addition is 4:3
So, (5x + 50)/(9x/2) = 4/3
Solving this equation, we get x = 22.

So, the initial number of literature books = 5x = 110
And the initial number of science books = 6x = 132
Therefore, the total number of books in the library = 110 + 132 = 242.

Since the question asks for the initial number of books (before the addition), the answer is option (B) 110.
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A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4thof the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?a)60b)110c)130d)140e)190Correct answer is option 'B'. Can you explain this answer?
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A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4thof the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?a)60b)110c)130d)140e)190Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4thof the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?a)60b)110c)130d)140e)190Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4thof the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?a)60b)110c)130d)140e)190Correct answer is option 'B'. Can you explain this answer?.
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