Q. 264.4( 8 Votes )

# In a survey of 20

Answer :

Given:

Total number of students = 200

Number of students study Mathematics = 120

Number of students study Physics = 90

Number of students study Chemistry = 70

Number of students study Mathematics and Physics = 40

Number of students study Mathematics and Chemistry = 50

Number of students study Physics and Chemistry = 30

Number of students study none of them = 20

Let U be the total number of students, P, M and C be the number of students study Physics, Mathematics and Chemistry respectively

To find: number of students who study all the three subjects n(M P C)

n(U) = 200, n(M) = 120, n(P) = 90, n(C) = 70, n(M P) = 40

n(M C) = 50, n(P C) = 30

Number of students who play either of them = n(P M C)

= Total – none of them

= 200 – 20

= 180……………(i)

Number of students who play either of them = n(P M C)

= n(C) + n(P) + n(M) – n(M P) – n(M C) – n(P C) + n(P M C)

= 120 + 90 + 70 – 40 – 30 – 50 + n(P M C)

= 160 + n(P M C)……………(ii)

From (i) and (ii):

160 + n(P M C) = 180

n(P M C) = 180 – 160

n(P M C) = 20

Hence, there are 20 students who study all three subjects.

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