Q13 of 71 Page 30

In a school 150 students passed X standard Examination. 95 students applied for Group I and 82 students applied for Group II in the Higher Secondary course. If 20 students applied neither of the two, how many students applied for both groups?

Given


total no student passed in X standard exam n(U) = 150


No of Students applied for Group I only n(A) = 95


No of Student applied for Group II only n(B) = 82


No of student applied for neither of the exam n(A∪B)' = 20


So No of student applied for exam n(A∪B) = n(U) – n(A∪B)'


= 150 – 20


= 130



From the above Venn diagram


(95–x) + x + (82–x) = 130


No of student applied for both the group x = (95 + 82) – 130


= 177 – 130


= 47


Number of students applied for both the group = 47.


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