In a certain production lot, 40 percent of the toys are red and the remaining toys are green.  Half of the toys are small and half are large.  If 10 percent of the toys are red and small, and 40 toys are green and large, how many of the toys are red and large?

To solve this problem, we need to break it down into several steps:

1. We know that 40% of the toys are red. This means that 60% of the toys are green.

2. We also know that half of the toys are large and half are small. So, 50% of the toys are large and 50% are small.

3. We are told that 10% of the toys are red and small.

4. We are also told that there are 40 toys that are green and large.

5. Since 50% of the toys are large and 60% of the toys are green, we can say that 30% of the toys are green and large.

6. If 30% of the toys are green and large and there are 40 such toys, we can calculate the total number of toys. Let's denote the total number of toys as T. So, 0.3T = 40. Solving for T, we get T = 40 / 0.3 = 133.33. Since the number of toys must be a whole number, we round this up to 134.

7. Now, we know that 40% of the toys are red and 50% of the toys are large. So, 20% of the toys are red and large.

8. To find the number of toys that are red and large, we multiply the total number of toys by this percentage: 0.2 * 134 = 26.8. Again, since the number of toys must be a whole number, we round this up to 27.

So, there are 27 toys that are red and large.