Question

In a college 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both
tea and coffee. Answer the following questions:
(i) How many students like only tea?
(ii) How many students like only coffee ?
(iii) How many students like neither tea or coffee?
(iv) How many students like at least one of the beverages?​

Answer 1

Total number of students who were randomly selected n(S) = 200

Number of students who like tea = 140

Number of students who like coffee = 120

Number of students who like both = 80

So,

Let the number of students who like tea be ' T '

Let the number of students who like coffee be ' C '

So given are :-

n(T)=140

n(C)=120

n(T∩C) =80

Venn Diagram

$\setlength{\unitlength}{1cm}\begin{picture}\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(2,0){\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)}\put(1,0){\bf{80}}\put(3,0){\bf{120}}\put(3,1){\bf{C}}\put(-1.5,0){\bf{140}}\put(-1,1){\bf{T}}\end{picture}$

Question

(i) How many students like only tea?

Number of students who like only tea = n(T) = 140 students

(ii) How many students like only coffee ?

Number of students who like only coffee = n(C) = 120 students

(iii) How many students like neither tea or coffee?

Number of students who like neither tea or coffee = n(S) - [n(T)+n(C) + n(T∩C)]

$\implies$ 200 - 340 , This is not possible so There are no students  students like neither tea or coffee

(iv) How many students like at least one of the beverages?​

All students like at least one beverage

                                                                             

Answer 2

Given:  In a college 200 students are randomly selected. 140 like tea, 120 like coffee, and 80 like both tea and coffee.

To find:  i) How many students like only tea?

             (ii) How many students like only coffee?

            (iii) How many students like neither tea or coffee?

            (iv) How many students like at least one of the beverages?​

Solution:

We can solve this problem by using Venn Diagrams.

People who like coffe= C= 120

People who like tea= T= 140

People who like both = C∩T=80

Students who like only tea= 140-80= 60

Students who like only coffee= 120-80= 40

Students who like neither= Total- Either likes coffee or tea

= 200- (140+120-80) = 200-180= 20

Students who like atleast  one= Total-none= 200-20= 180

(i) How many students like only tea= 60

(ii) How many students like only coffee= 40

(iii) How many students like neither tea or coffee=20

(iv) How many students like at least one of the beverages= 180