Question

There were $5400$ books in a library. The ratio of the number of fiction books to the number of classics to the number of biographics was $7:3:2$. When the library acquired an additional $432$ books, the number of biographies increased by $12\%$ and the number of classics increased by $10\%$. The percentage increase in the number of fiction books is

• A. $8\%$
• B. $4\%$
• C. $6\%$
• D. $9\%$

Answer 1

Answer: (C)

$6\%$

Given There were $5400$ books in a library.The ratio of the number of fiction books to the number of classics to the number of biographics was $7:3:2.$
Then number of fiction books=$\frac{5400\times 7}{12}=3150$

The number of classics=$\frac{5400\times 3}{12}=1350$

The number of biographics=$\frac{5400\times 2}{12}=900$

The number of biographies increased by $12$%
Then number of biographies Books=$\frac{900\times 112}{100}=1008$

and the number of classics increased by $10$%.
Then number of classics Books =$\frac{1350\times 110}{100}=1485$

When the library acquired an additional $432$ books,
Then totan books in library =$5400+432=5832$
Then number of fiction books=$5832-1008-1485=3339$
Then increase in fiction books=$3339-3150=189$
Then % of increase in fiction books=$\frac{189\times 100}{3150}=6$%