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$1000$ patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines $\text{-A, B, C}$ and $\text{D}$. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.

  1. A total of $250$ patients were treated with type $\text{A}$ medicine and a total of $210$ patients were treated with type $\text{C}$ medicine.
  2. $25$ patients were treated with type $\text{A}$ medicine only. $20$ patients were treated with type $\text{C}$ medicine only. $10$ patients were treated with type $\text{D}$ medicine only.
  3. $35$ patients were treated with type $\text{A}$ and type $\text{D}$ medicines only. $20$ patients were treated with type $\text{A}$ and type $\text{B}$ medicines only. $30$ patients were treated with type $\text{A}$ and type $\text{C}$ medicines only. $20$ patients were treated with type $\text{C}$ and type $\text{D}$ medicines only.
  4. $100$ patients were treated with exactly three types of medicines.
  5. $40$ patients were treated with medicines of types $\text{A, B}$ and $\text{C}$, but not with medicines of type $\text{D}$. $20$ patients were treated with medicines of types $\text{A, C}$ and $\text{D}$, but not with medicines of type $\text{B}$.
  6. $50$ patients were given all the four types of medicines. $75$ patients were treated with exactly one type of medicine.

How many patients were treated with medicine type $\text{B}$?

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