Question

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

Answer 1

24 experts

Explanation:

As shown in the diagram,we let

U=[Total number of experts who voted]

`\implies n(U)=x`

This implies that the number of experts who voted for Mr A in terms of x is

`(1)/(2)x`

And in terms of x, the number of experts who voted for Mr B is

`(2)/(3)x`

From the diagram, we can write the below equation,

`x= (1)/(2)x - 10 + 10 + (2)/(3)x - 10 + 6`

`x - (1)/(2)x - (2)/(3)x = 4`

We multiply through by the L.C.M (is that 6) to get,

`6x - 3x - 2x = 24`

`x = 24`