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Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A survey has been conducted on methods of commuter travel. Each respondent was asked to check Bus, Train or 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?
Solution
Let Bus, Train and Automobile be represented by $B,T,A$ respectively.
Given,
$n(B)=30$
$n(T)=35$
$n(A)=100$
$n(B\cap T)=15$
$n(B\cap A)=15$
$n(T\cap A)=20$
$n(B\cap T\cap A)=5$
Using the formula,
$n(B\cup T\cup A)=n(B)+n(T)+n(A)-n(B\cap T)-n(B\cap A)-n(T\cap A)+n(B\cap T\cap A)$
Now,
$n(B\cup T\cup A)=30+35+100-15-15-20+5$
$=165-50+5$
$=120$
Therefore, $120$ people completed the survey form.
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