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.

Question

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?

Accepted Answer

6600 — Easy Let $f$ be the 2010 fiction count. The total growth ($10\%$ on $f$, $12\%$ on the rest) must equal the actual increase of $1260$ books. Solve the single linear equation for $f$, then grow it by $10\%$. 1 Find the total increase. Books rose from $11500$ to $12760$. $$\begin{aligned} &\Delta=12760-11500=1260 \end{aligned}$$ 2 Set up the growth equation. Fiction $f$ grows $10\%$; non-fiction $(11500-f)$ grows $12\%$; together they add $1260$ (step 1). $$\begin{aligned} &0.10\,f+0.12\,(11500-f)

CAT 2019 Slot 2 — QA Question 9

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