Question

36. In a beauty contest, half the number of experts voted for Mr. A and two thirds votedfor Mr. B. 10 voted for both and 6 did not vote for either. How many experts werethere in all?​

Answer 1

Answer

not defining the notations,

let the number of experts be x

given

n(A) = x/2

n(B) = 2x/3

n(AnB) = 10

n(AuB) = n(A) + n(B) - n(AnB)

= x/2 + 2x/3 - 10

= (3x + 4x - 60)/6

= (7x - 60)/6

now 6 experts did not vote (why were they present there anyway!!!!)

so. n(U) = (7x - 60)/6 + 6

this is equal to total no. of experts

(7x - 60)/6 + 6 = x

7x - 60 + 36 = 6x

7x - 6x = 60 - 36

x = 24.