125, 100 and 145 students appeared at post graduate examination in certain University in the subjects economics, hindi, and commerce respectively. 25 students appeared in economics only, 30 appeared in economics & hindi, 80 in economics & commerce and 60 appeared in hindi & commerce. Use Venn diagram to find the number of students who appeared in all the subjects, in hindi only and in commerce only
Answers
All Subjects = 10 , Hindi only = 20 & Commerce only = 15
Step-by-step explanation:
Economics E = 125
Hindi H = 100
Commerce C = 145
Economics only = 25
Economics & Hindi = E ∩ H = 30
Economics & Commerce = E ∩ C = 80
Hindi & Commerce = C ∩ H = 60
All subject E ∩ H ∩ C = ?
Economics only = E - E ∩ H - E ∩ C + E ∩ H ∩ C
=> 25 = 125 - 30 - 80 + E ∩ H ∩ C
=> E ∩ H ∩ C = 10
Hindi only = H - E ∩ H - H ∩ C + E ∩ H ∩ C
=> Hindi only = 100 - 30 - 60 + 10
=> Hindi only = 20
Commerce only = C - E ∩ C - H ∩ C + E ∩ H ∩ C
=> Commerce only = 145 - 80 - 60 + 10
=> Commerce only = 15
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