UGC NET CSE | December 2018 | Part 2 | Question: 4

Question

​​​​​​A survey has been conducted on methods of commuter travel. Each respondent was asked to check Bus, Train and Automobile as a major method of travelling to work. More than one answer was permitted. The results reported were as follows :

Bus $30$ people; Train $35$ people; Automobile $100$ people; Bus and Train $15$ people; Bus and Automobile $15$ people; Train and Automobile $20$ people; and all the three methods $5$ people. How many people completed the survey form?

• A. $120$
• B. $165$
• C. $160$
• D. $115$

Comments

option A 100+35+30-15-15-20+5=120

Answer 1

n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(C∩A)+n(A∩B∩C)

n(A∪B∪C)=30+35+100-15-20-15+5

n(A∪B∪C)=120

A=Bus

B=Train

C=Automobile

Option (A)

Answer 2

Let  ‘A’ denotes people travelled by Bus  ,  30 people

Let  ‘B’ denotes people travelled by Train,     35 people

Let  ‘C’ denotes people travelled by Automobile,    100 people

Let   ‘A∩B’ denotes people travelled by bus and Train ,   15 people

Let   ‘A∩C’ denotes people travelled by bus and Automobile,    15 people

Let   ‘B∩C’  denotes people travelled by   Train and Automobile,    20 people

Let   ‘A∩B∩C’ denotes people travelled by Bus , Train and Automobile , 5 people

Number of people completed the survey

=A+B+C-(A∩B)-(A∩C)-(B∩C)+(A∩B∩C)

=30+35+100-15-15-20+5

=120

So option A  is correct answer