Question 1209416
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The ratio of women to men in group P is 11:4, so let the numbers of women and men be 11x and 4x.<br>
The ratio of women to men in group Q is 1:1, so let the numbers of women and men be y and y.<br>
The total number of people in group P is 15x; the total number in group Q is 2y.  Those two numbers 15x and 2y must be equal positive integers.  The smallest values of x and y that satisfy that condition are x=2 and y=15.<br>
So in group P there are 11x = 22 women and 4x = 8 men; in group Q there are y = 15 women and y =15 men.  The total number of women is 22+15 = 37; the total number of men is 8+15 = 23.<br>
ANSWER: 37:23<br>