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.**

Rate this question :

Mark the correct RD Sharma - Mathematics

Mark the correct RD Sharma - Mathematics

If A and B are twRD Sharma - Mathematics

If A and B are twRD Sharma - Mathematics

A survey shows thRD Sharma - Mathematics

If A = {x : x <spRS Aggarwal - Mathematics

Mark the correct RD Sharma - Mathematics

In a group of 70 RD Sharma - Mathematics

If P and Q are twRD Sharma - Mathematics