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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