Ratio P6 2011 Nanyang SA2 P2 Q18

18. In a cinema, the ratio of the number of girls to the number of boys was 3 : 2. The ratio of the number of women to the number of boys was 5 : 4. The ratio of the number of girls to the number of men was 2 : 5. During the movie, 6 women and 27 men left the cinema. The ratio of the number of women to the number of men then became 1 : 2.
(a) Express the number of women as a fraction of the number of men at first. Leave your answer in its simplest form.
(b) How many children were there in the cinema?
Answer given: (a) 1/3 and (b) 30

          x 2

3 : 2   =   6 : 4

5 : 4

          x 3
2 : 5   =  6 : 15

5 /15  =  1/3

a) It was  1/3.

  W       M          W x 2

----------------------------
5        :   15         10               {Use to 5 : 15 instead of 1 : 3}
- 6     - 27       - 12
----------------------------
  1   :    2           2
----------------------------

15 u – 27  à 10 u – 12

5 u à 27 – 12 = 15

1 u à 15/5 = 3

10 u à 10 x 3 = 30

b) It was 30 children.