Q. 135.0( 1 Vote )

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?

Answer :

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(AB)' = 20


So No of student applied for exam n(AB) = n(U) – n(AB)'


= 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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