Ratio Problem: Fiction vs Non-Fiction Books

This question asks us to find the number of non-fiction books based on a given ratio and the number of fiction books.

Given Information

• The ratio of fiction books to non-fiction books is $4 : 3$.
• The number of fiction books is 240.

Objective

We need to determine the total count of non-fiction books.

Calculation Steps

1. Understand the ratio:

   The ratio $4 : 3$ means that for every 4 fiction books, there are 3 non-fiction books.

   We can express this relationship as a fraction:

   $ \frac{\text{Number of Fiction Books}}{\text{Number of Non-Fiction Books}} = \frac{4}{3} $

2. Set up the proportion:

   Let $N$ represent the unknown number of non-fiction books.

   Substitute the known values into the fraction:

   $ \frac{240}{N} = \frac{4}{3} $

3. Solve for N (Number of Non-Fiction Books):

   To find $N$, we can use cross-multiplication:

   $ 4 \times N = 240 \times 3 $

   Calculate the product on the right side:

   $ 4N = 720 $

   Now, isolate $N$ by dividing both sides by 4:

   $ N = \frac{720}{4} $

   Perform the division:

   $ N = 180 $

   Alternatively, we can rearrange the equation $\frac{240}{N} = \frac{4}{3}$ to solve for $N$ directly:

   $ N = 240 \times \frac{3}{4} $

   Calculate the result:

   $ N = (240 \div 4) \times 3 $

   $ N = 60 \times 3 $

   $ N = 180 $

Conclusion

Based on the ratio and the number of fiction books, there are 180 non-fiction books in the school library.