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In a beauty contest, half the number of experts voted Mr. A and two thirds voted for Mr. B 10 voted for both and 6 did not for either. How may experts were there in all.





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Solution


Let the total number of experts be N.
E is the set of experts who voted for miss A.
F is the set of experts who voted for miss B.
Since 6 did not vote for either, n(EF)=N6.
n(E)=N2,n(F)=23N and n(EF)=10
.
So, N6=N2+23N10
Solving the above equation gives 


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