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(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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