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

Answer

24 experts

Step-by-step 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

$\frac{1}{2}x$

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

$\frac{2}{3}x$

From the diagram, we can write the below equation,

$x= \frac{1}{2}x - 10 + 10 + \frac{2}{3}x - 10 + 6$

$x - \frac{1}{2}x - \frac{2}{3}x = 4$

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

$6x - 3x - 2x = 24$

$x = 24$