Question

In a class of 600 boys. 75%play hockey and 45% play football. How many of tjem play both

Answer 1

Notice that "7 play both Hockey and Cricket" does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Hockey/Football.

{Total}={Hockey}+{Cricket}+{Football}−{HC+CH+HF}+{All three}+{Neither}{Total}={Hockey}+{Cricket}+{Football}−{HC+CH+HF}+{All three}+{Neither} 
(For more check ADVANCED OVERLAPPING SETS PROBLEMS)

50=20+15+11−(7+4+5)+{All three}+1850=20+15+11−(7+4+5)+{All three}+18;
{All three}=2{All three}=2;

Those who play ONLY Hockey and Cricket are 7 - 2 = 5;
Those who play ONLY Cricket and Football are 4 - 2 = 2;
Those who play ONLY Hockey and Football are 5 - 2 = 3;

Hence, 5 + 2 + 3 = 10 students play exactly two of these sports.

Answer: B. 
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Hope This helps :)

Answer 2

The total number of students in the class n(AUB) = 600.

75% play hockey.

n(A) = 75/100 * 100

        = 450

45% play Football.

n(B) = 45/100 * 600

        = 270.


Now,

Boys Who play both the games = 450 + 270 - 600

                                                     = 120.


Hope this helps!