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There are 70 patients in a naturopathy hospital. It has three facilities (clay/steam/oil bath). 15 chose a clay and oil bath. 8 chose clay and steam bath. 9 chose oil and steam bath. 35 chose only 1 type of bath. How many chosen all three types of the bath?

There are 70 patients in a naturopathy hospital. It has three facilities (clay/steam/oil bath). 15 chose a clay and oil bath. 8 chose clay and steam bath. 9 chose oil and steam bath. 35 chose only 1 type of bath. How many chosen all three types of the bath? Correct Answer 3

Given:

Total number of patients = 70

Concept used:

Ven diagram

Calculation:

[ alt="F1 Arun Shraddha 10-02-2022 D1" src="//storage.googleapis.com/tb-img/production/22/02/F1_Arun_Shraddha_10-02-2022_D1.png" style="width: 174px; height: 208px;">

In the given ven diagram

We can see 15 is in Clay and Oil

8 is in Clay and Steam

9 is in Oil and Steam

And as in the question, nothing is mentioned about 35 we have divided it into 10, 12, 13

So, 

No. of patients who chose all three = 70 - (15 + 8 + 9 + 35)

⇒ 3

∴ Requried answer is 3

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