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In a beauty contest, half the number of judges voted for Miss A, 2/3 of them voted for

Miss B,10 voted for both and 6 did not vote for either of them. Find how many
judges in all, were present?


Let the number of judges be x, then from the given information we have n(A) = \dfrac{x}{2},  n(B) = \dfrac{2x}{3},  n(A \cap B) = 10 and  n(A' \cap B') = 6 

 x = n(A) + n(B) - n(A\cap B) +n(A'\cap B') 
 x = \dfrac{x}{2}+ \dfrac{2x}{3}- 10+6 

It is easy to solve x.
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