During a survey, some people responded that they liked fencing to other sports. The ratio of the number of people who liked fencing to those who disliked it was 3 : 1. The ratio of the number of men to the number of women who liked fencing was 1 : 5. If 10% of the people who disliked fencing were men, what was the ratio of the number of men to the number of women chosen for the survey?
Liked |
Disliked |
3 u |
1 u |
Men |
Women |
Men |
Women |
1 |
5 |
1 |
9 |
0.5 u |
2.5 u |
0.1 u |
0.9 u |
10% =
10100 =
110 Number of men who liked fencing
=
16 x 3 u
= 0.5 u
Number of women who liked fencing
= 3 u - 0.5 u
= 2.5 u
Number of men who disliked fencing
=
110 x 1 u
= 0.1 u
Number of women who disliked fencing
= 1 u - 0.1 u
= 0.9 u
Total number of men
= 0.5 u + 0.1 u
= 0.6 u
Total number of women
= 2.5 u + 0.9 u
= 3.4 u
Women : Men
0.6 : 3.4
(x5)3 : 17
Answer(s): 3 : 17