In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Solution:

Let U be the set of all students who took part in the survey T be the set of students taking tea.

C be the set of students taking coffee.

Students taking neither tea nor coffee, (T' ∩ C')

It is given that

n (U) = 600, n (T) = 150, n (C) = 225, n (T ∩ C) = 100

We know that

n (T' ∩ C') = n (T υ C)'

= n (U) - n (T υ C)

= n (U ) - [n (T) + n (C) - n (T ∩ C)]

= 600 – [150 + 225 - 100]

= 600 - 275 

= 325

Hence, 325 students were taking neither tea nor coffee.

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NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 13

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Summary:

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee is given. We have found that 325 students were taking neither tea nor coffee