Solving the following mathematical problems:

70 students are studying physics, mathematics and chemistry. 40 students study mathematics, 35 study physics and 30 study chemistry, 15 students are studying all the subjects. How many students are studying exactly two of the subjects?

Created: 3 months ago | Updated: 3 months ago

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Given, total students = 70

M=40; P= 35; C = 30 [Using first alphabet of all subjects]

P+C+M=15

Now, we can solve it by using Venn diagram. Let depict it.

We let the number of students

who study exactly two subjects are x, y & z.

We have to find out the value of (x + y + z)

According to the question

$40 - 15 - x - y + 35 - 15 - x - z + 30 - 15 - y - z + x + y + z + 15 = 70 \Rightarrow 105 - 30 - x - y - z = 70 \Rightarrow 75 - 70 = x + y + z x + y + z = 5$
The number of students studying exactly two subjects is 5.

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