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Question:

How many patients were treated with medicine type B?

Explanation:

We can draw the following Venn diagram according to the information given in the question.

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75 patients were treated with exactly one type of medicine.
∴ 25 + a + 20 + 10 = 75
⇒ a = 20

250 patients were treated with type A medicine
∴ 25 + 30 + 20 + 35 + 20 + 40 + 50 + e = 250.
⇒ e = 30

100 patients were treated with exactly three types of medicines.
∴ 20 + 40 + c + e = 100
⇒ c = 10

210 patients were treated with type C medicine
∴ 30 + 40 + b + 20 + 20 + 50 + c + 20 = 210
⇒ b = 20

Since patients were equally in treatment group and control group hence, there were total 500 patients who were in the treatment group and 500 in control group (who were not given any medicine).

Total patient in treatment group = 500 = 25 + 30 + 20 + 35 + 20 + 40 + 50 + e + a + b + c + d + 20 + 20 + 10.
⇒ d = 150

The completed Venn diagram:

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∴ 340 patients were treated with Type B medicine.

Hence, 340.