NIMCET 2019 Question Paper with solutions

Question : 47 of 120

Marks: +1, -0

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

18
36
24
None

Validate

Solution:

Let the total numbers of expert in beauty contest is x

n(A)=x/2

n(B)=2/3x

n(A∩B)=10

n(A∪B)'=6

n(A∪B)=x-n(A∪B)'=x-6

n(A∪B)=n(A)+n(B)-n(A∩B)

x-6=x/2+{2x}/3-10

x-x/2-{2x}/3=-10+6

{6x-3x-4x}/6=-4

x=24

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