Question

In a beauty contest, half the number of experts voted for Miss. A and two thirds voted for Miss B, 10 voted for both and '6' did not vote for either. Then how many experts were there in all is

• A. 20
• B. 24
• C. 22
• D. 26

Answer 1

Answer: (B)

24

Answer 2

Let the number of experts = x $n\left(A\right) = \frac{x}{2}.n\left(B\right)= \frac{2x}{3}$ $n\left(A\cap B\right) = 10, n\left(A^{C}\cap B^{C}\right) = 6$ $n\left(A\cup B\right) = \frac{x}{2} + \frac{2x}{3} - 10$ $n\left(A^{C}\cap B^{C}\right) = 6 \Rightarrow n\left(\mu\right) -n\left(A\cup B\right) = 6$ $\Rightarrow x - \frac{x}{2} - \frac{2x}{3} + 10 = 6$ $\Rightarrow 6x -3x -4x + 60 = 36$ $\Rightarrow x = 24$