Question

In a village ,every weekend, three-eighth of the men and one third of the woomen participate in social activity.if the total number of participants is 54, and out of them 18 are men then the total number of men and women in the village is

Answer 1

Let x be the number of men in the village

Let y be the total number of women

Given the fraction of men participating in the social activity =$\frac{3}{8}$

the fraction of women participating in the social activity = $\frac{1}{3}$

We know that 18 men are the participants

that is three-eighths of the total number of men is 18

ie.$\frac{3}{8} of x = 18$

$\frac{3}{8} .x=18$

$x =\frac{144}{3}$

$x=48$

Hence the number of men is 48

Now out of 54 participants 18 are men and hence the number of women participants are 54-18 = 36

We already know that one-third of the total women are participants and hence it is equal to 36

$\frac{1}{3} of y = 36$

$y= 36.\frac{3}{1}$

$y=108$

So the total number of men and women are 48+108 = 156