Soccer league participation

user123321 wrote:last year say we have
m men,w women & m+w total
but this year
1.05m men,1.2w women & 1.1(m+w) total

since sum of men and women should tally to total..
1.05m + 1.2w = 1.1(m+w)
0.05m = 0.1w
w/m = 1/2
=>w/(w+m) = 1/3

so 1/3 or 33% are females in the league now

user123321

Ian Stewart wrote: That's not quite right, and if the source says that's the right answer (where is it from?) then there's a problem with their solution. The question asks for the proportion of participants who are women *now* in the league. In the solution above, m and w represent the number of men and women *last year*, not this year. We need to apply the percent increases in the question first to get the answer: we have that m = 2w, so there are 1.2w women in the league now, and (1.05)(2w) = 2.1w men in the league now, so women make up 1.2w/(1.2w + 2.1w) = 12/33 = 4/11 of all participants this year.

You can certainly use alligation here provided you understand what the answer you get means. We have two groups, one of which increased by 5%, the other by 20%, and the overall increase was 10%. So on a number line we have:

--5-------10-------------------20---

The distances to the middle are 5 and 10, so the ratio of the two groups *before the increases* was 5 to 10, or 1 to 2. Since the overall increase is closer to 5%, we must have more men, so the league was 2/3 men and 1/3 women before the increases. Now we can get the answer by applying the percent increases in the question, just as I did above.