Question

In a class 50 students. Each one come to school by bus or by bicycle or on foot. 25 by bus 20 by bicycle 30 on foot and 10 students by all the the three now how many students come to school exactly by two mode of transport

Answer 1

5 students come to school exactly by two modes of transport.

Given :

Total number of students = 50

Number of students who come to school by bus = n(A)= 25

Number of students who come to school bicycle = n(B) = 20

Number of students who come to school on foot = n(C) = 30

Total number of students = n(A∪B∪C) = 50

Number of students who come to school by all three modes of transport - n(A∩B∩C) = 10

Using formula-

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

50 = 25 + 20 +30 - n(A∩B) - n(B∩C) - n(C∩A) + 10

50 = 85 - n(A∩B) - n(B∩C) - n(C∩A)

n(A∩B) - n(B∩C) - n(C∩A) = 85 - 50

n(A∩B) - n(B∩C) - n(C∩A) = 35

Finding the students who come exactly by two modes :-

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

= (A∩B + B∩C + C∩A ) - 3 *(A∩B∩C)

= 35 - 3(10)

= 35 - 30

= 5

Hence : Number of students who come to school by two modes of transport = 5