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    Q. 10:  Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is

    A.  75
    B.  80
    C.  60
    D.  70

    Video Explanation

    Explanatory Answer

    From observing the data given, we find that it is a closed 3 set Venn diagram.

    Let the three sports be F, T and C for Football, Tennis and Cricket respectively
    n(FUTUC) = 256 , n(F) = 144, n(T) = 123, n(C) = 132, n(F T) = 58, n(C ∩T) = 25, n(F C) = 63

    We know that (AUBUC) = n(A) + n(B) +n(C) – n(A B) – n(B ∩C) – n(C A) + n(A ∩B C)
    So, 256 = 144 + 123 + 132 – 58 – 25 – 63 + n (F T ∩C)
    n (F T C) = 256 – 144 + 123 +132 – 146


    n (F T C) = 256 – 253 = 3
    Now, it is easy to calculate the number of students who only play tennis using a Venn diagram.
    n (Students who play only Tennis) = 123 – (55 + 3 + 22) = 123 – 80
    n (Students who play only Tennis) = 43 students

    Enquiry