Percentage problem 4 by Dhaval Furia

Algebra Level pending

In 2010 2010 , a library contained a total of 11500 11500 books in two categories - fiction and nonfiction . In 2015 2015 , the library contained a total of 12760 12760 books in these two categories. During this period, there was 10 % 10\% increase in the fiction category while there was 12 % 12\% increase in the non-fiction category. How many fiction books were in the library in 2015 2015 ?

6000 6000 6160 6160 5500 5500 6600 6600

Dhaval Furia by Dhaval Furia , 26, India

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1 solution

Let in the year 2010 2010 , the number of fiction books be f f . Then

f ( 1 + 10 100 ) + ( 11500 − f ) ( 1 + 12 100 ) = 12760 ⟹ f = 120 × 50 = 6000 ⟹ 11 f 10 = 6600 f(1+\frac{10}{100})+(11500-f)(1+\frac{12}{100})=12760\implies f=120\times 50=6000\implies \dfrac{11f}{10}=6600 .

Hence the number of fiction books in the year 2015 2015 was 6600 \boxed {6600} .

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