In a group of 160 people, men and women are in the ratio of 3 : 1. After adding some women in the group, the ratio becomes 2 : 1. The mean of weights of the group is 64 kg and the average of women's weights is 3 kg more than men's. A. The mean weight of men in the group is 63 kg. B. The mean weight of men in the group is 65 kg. C. The mean weight of women in the group is 66 kg. D. The mean weight of women in the group is 68 kg. E. The mean weight of women in the group is 65 kg. Which of the above statements is/are correct?

From the initial ratio of 3 to 1 for 160 people, there are 120 men and 40 women. Let the mean weight of men be m and the mean weight of women be m plus 3, then set up the equation for the total weight as 120m plus 40 times the quantity of m plus 3 equals 160 times 64. This simplifies to 160m plus 120 equals 10240, so 160m equals 10120, and solving for m gives 63.25. The mean weight of men is 63.25 kg, making the mean weight of women 66.25 kg, so the statements claiming 63 kg for men and 66 kg for women are correct.

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