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Library books percentage increase

CAT 2019 Slot 2 · Quantitative Ability · Medium · Percentages

This is a medium Quantitative Ability question from the CAT 2019 Slot 2 paper. It tests Percentages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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

  1. A.

    6600

  2. B.

    6160

  3. C.

    6000

  4. D.

    5500

Answer

A

Explanation

Let FF and NN be the number of fiction and non-fiction books in 2010, respectively. F+N=11500F + N = 11500 1.1F+1.12N=127601.1F + 1.12N = 12760

Multiply the first equation by 1.11.1: 1.1F+1.1N=126501.1F + 1.1N = 12650

Subtract this from the second equation: 0.02N=110  ⟹  N=55000.02N = 110 \implies N = 5500

Then F=11500−5500=6000F = 11500 - 5500 = 6000.

The number of fiction books in 2015 =1.1F=1.1×6000=6600= 1.1F = 1.1 \times 6000 = 6600.

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