In a beauty contest, half the number of experts voted Mr. A and two thirds vo...

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Question Id : 3896 | Context : NIMCET 2019

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.

🎥 Video solution / Text Solution of this question is given below:

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

(E \cup F) = N - 6

n (E) = \frac{N}{2}, n (F) = \frac{2}{3} N

and

n (E \cap F) = 10

.
So,

N - 6 = \frac{N}{2} + \frac{2}{3} N - 10

Solving the above equation gives

\frac{N}{6} = 4 \Rightarrow N = 24

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