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In a Hostel, 76% of the total students use Desktop and 64% of the total students use laptop. What is the maximum percentage of students using both Desktops and Laptops

A.
40%
B.
64%
C.
76%
D.
88%

Solution:

Calculation:? n(D) = 76%, n (L) = 64%? n(D ? L) = n (D) + n (L) “ n (L ? D)Case I: If every student uses at least 1 item ? n(D ? L) = 100% = 76% + 64% - n (L ? D)? n( L ? D) = 140 “ 100 = 40%Case II: If some do not use either of the two ? Max (L ? D) = showing all using desktop, uses laptop also. i.e. 64%? 40% ? n (L ? D) ? 64%? Maximum percentage of students using both Desktops and Laptops = 64%Additional Information? If we want to maximize those who use both, we have to maximize the value in the intersection. So, we have to minimize the value of the union.? If we want to minimize those who use both, we have to minimize the value in the intersection. So, we have to maximize the value of the union.

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