In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct?

1. At least 30 Indian participants are vegetarian.

2. At least 10 Indian participants are non-vegetarian.

Select the correct answer using the codes given below:

The correct option is Both 1 and 2.

Let us analyze the given information step-by-step to understand why both statements are correct:
Total number of participants = 100
Number of Indian participants = 70
Therefore, the number of non-Indian participants is:
$$100-70=30$$

We are also given the food habits of the participants:
Number of vegetarian participants = 60
Therefore, the number of non-vegetarian participants is:
$$100-60=40$$

Evaluating Statement 1: At least 30 Indian participants are vegetarian.
To find the minimum possible number of Indian participants who must be vegetarian, we need to make as many non-Indians vegetarian as possible.
Since there are only 30 non-Indian participants in total, the maximum number of non-Indians who can be vegetarian is 30.
Subtracting this maximum from the total number of vegetarians gives the minimum number of Indian vegetarians:
$$\text{Minimum Indian vegetarians}=60-30=30$$ Thus, at least 30 Indian participants are vegetarian. Statement 1 is correct.

Evaluating Statement 2: At least 10 Indian participants are non-vegetarian.
To find the minimum possible number of Indian participants who must be non-vegetarian, we need to make as many non-Indians non-vegetarian as possible.
Since there are only 30 non-Indian participants in total, the maximum number of non-Indians who can be non-vegetarian is 30.
Subtracting this maximum from the total number of non-vegetarians (40) gives the minimum number of Indian non-vegetarians:
$$\text{Minimum Indian non-vegetarians}=40-30=10$$ Thus, at least 10 Indian participants are non-vegetarian. Statement 2 is also correct.

Since both Statement 1 and Statement 2 are correct, the correct option is "Both 1 and 2".