Comprehension:
A speciality supermarket sells $320$ products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU.
The following facts are also known:
1. There were equal numbers of domestic and foreign products.
2. Half of the domestic products were FDA approved cosmetic products.
3. None of the foreign products had both the approvals, while $60$ domestic products had both the approvals.
4. There were $140$ nutrition products, half of them were foreign products.
5. There were $200$ FDA approved products. $70$ of them were foreign products and $120$ of them were cosmetic products.
Which among the following options best represents the number of domestic cosmetic products that had both the approvals?
- At least $10$ and at most $80$
- At least $10$ and at most $60$
- At least $20$ and at most $70$
- At least $20$ and at most $50$