A baker makes 20 loaves of bread each day. The loaves are either white or brown. The ratio of white loaves to brown loaves is $6:4$. We need to find out after how many days the baker would have made 240 loaves of brown bread.

1. Problem Description

A baker makes 20 loaves of bread each day. The loaves are either white or brown. The ratio of white loaves to brown loaves is $6:4$. We need to find out after how many days the baker would have made 240 loaves of brown bread.

2. Solution Steps

First, we need to find the number of brown loaves made each day. The ratio of white to brown loaves is $6:4$. This means for every 10 loaves, 6 are white and 4 are brown.

The total number of parts in the ratio is $6 + 4 = 10$.

The fraction of brown loaves is $\frac{4}{10}$.

Since the baker makes 20 loaves of bread each day, the number of brown loaves made each day is:

$\frac{4}{10} \times 20 = \frac{4 \times 20}{10} = \frac{80}{10} = 8$

So, the baker makes 8 brown loaves each day.

To find the number of days it takes to make 240 loaves of brown bread, we divide the total number of brown loaves (240) by the number of brown loaves made each day (8).

Number of days = $\frac{240}{8} = 30$

3. Final Answer

30 days