    Question

# In a class of 175 students the following data shows the number of students one or more subjects. Mathematics 100 ; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23 ; Mathematics ,Physics and Chemistry 18. How many students have offered Mathematics alone ?

A

35

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B

48

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C

60

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D

22

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Solution

## The correct option is A 60 Let M be the set of students who study mathematics, P be the set of students who study physics and C be the set of students who study chemistry. Then, n(U) = 175, n(M)= 100, n(P)= 70 and n(C) = 40 n(M∩P)=30,n(M∩C)=28 and n(P∩C)=23 n(M∩P∩C)=18 ∵n(M)=100 ⇒a+b+e+f=100 ....(i) Now n(P) = 70 ⇒b+c+d+e=70 ....(ii) Now n(C) = 40 ⇒ f+e+d+g = 40 ....(iii) Now n(M∩P)= 30 ⇒ b+ e = 30 ....(iv) Now n(M∩P) = 28 ⇒ e +f = 28 ....(v) Now n(P∩C)= 23 ⇒ d + e = 23 ....(vi) Now n(M∩P∩C)= 18 ⇒ e = 18 ....(vii) from Equation (vi) and (vii), d = 5 from Equation (v) and (vii), f = 10 from Equation (iv) and (vii), b = 12 On substituting the value of b, e, f in equation (i) we get ⇒a+b+e+f=100 a+12+18+10= 100 a= 60 ....(c)  Suggest Corrections  16      Related Videos   Cardinal Properties
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