Question

During a survey, some people responded that they preferred badminton to other sports. The ratio of the number of women to the number of men who liked badminton was 3:1. The ratio of the number of people who liked badminton to those who disliked it was 3:1. If 20% of the people who did not like badminton were women, what was the ratio of the number of men to the number of women chosen for the survey?

Answer 1

Suppose the number of men who liked badminton was x,
the number of men who disliked badminton was x,
the number of women who liked badminton was y,
the number of women who disliked badminton was y,
y1/x1 = 3/1 - - - - (1)
(x1 + y1)/(x2 + y2) = 3/1 - - - - (2)
y2/(x2 + y/2) = 1/5 - - - - (3)
(1) -> y1 = 3x1 - - - - (4)
(3) -> y2 = 1/4x2 - - - - (5)
Substitute (4) and (5) into (2)
(x1 + 3x1)/(x2 + 1/4x2) = 3/1 => x1 = 15/16x2
The ratio of the number of men to the number of women chosen for the survey = (x1 + x2)/(y1 + y2) = (x1 + x2)/(3x1 + 1/4x1) = (15/16x2 + x2)/(3 * 15/16x2 + 1/4x2)
= (x 31/16x2)/49/16x2
= 31/49
= 31:49