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Bunuel
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Bunuel
There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 45% play football, how many play both?

(A) 48
(B) 60
(C) 80
(D) 120
(E) 150

IMO the answer is option D

As per the formula,
Total- neither = hockey + football - both
600-0= 75% of 600 + 450% of 600 -both
600=450+270-both
Both=120
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Note that each person plays either hockey or football. This implies |AUB| = 600

We know, |AUB| = |A| + |B| - |A∩B|

=> 600 = (75% of 600) + (45% of 600) - |A∩B|

=>. |A∩B| = 120

Hence (D) is the answer.

Glad to help!
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hi can anyone show this by double matrix method?
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