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Question

At first, the ratio of the number of men to the number of women in a fun fair was 4:5. When 36 woman and some men joined in the fun fair, there was a 12% increase in the number of women and the total number of people was increased by 20%.

a) How many men were there at first?

b) What was the percentage in crease in the number of men after 36 women and some men joined in the fun fair?

Answer

Women at first –> 100% (5u)

Women in the end –> 112%

12% –> 36

1% –> 36/12

      = 3

women at first = 100%

                            = 300

5u = 300

1u = 300/5

     = 60

a) Men at first = 4u

                            = 4×60

                            = 240

b) Total at first = 9u

                             = 9×60

                             = 540

     Total in the end = 120% x 540

                                   = 648

     Men in the end = 648-300-36

                                   = 312

     % increase in men = (312-240) /240 x 100%

                                         = 30%

 

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Suggested answer:

At first, ratio of men to women is 4 : 5.

When 36 women join, no of women increased by 12%.

12% –> 36

100% –> 36/12 x 100 = 300

At firsts, no of women is 300.

At firsts, no of men will be:

300 / 5 x 4 = 240

a) There were 240 men at first.

Total people at first is 240 +300 = 540.

20% increase => 540 x 20% = 108

Increase in men will be 108 – 36 = 72

Percentage of increase in men will be,

72 / 240 x 100% = 30%

b) Percentage of increase in men was 30%

 

 

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