Percentage of a percentage - Wiki

  • #percentageofapercentage
    • There was a group of `80` pupils in the hall. 40% of them were girls. When some more girls joined the group, the percentage of boys decreased to 20%. How many pupils were there in the end?
      • #percentageofapercentage

        Original no. of girls

        80 `xx` `40/100`  = 32

        Original no. of boys

        80 `xx` `60/100`  = 48

        The percentage of boys in the end

        20%

        20% = 48

        No. of pupils in the end

        100% = 48 `-:` 2 `xx` 10 = 240    

    • At a fun-raising event, 60% of the people were male and the rest were female. 20% of the female left the event in the afternoon. In the evening, after 33 male and 35 female left the event, 75% of the people at the event were male. a) What percentage of the people left the event in the afternoon? b) How many people were there at the start of the fun raising event? Ans: a) _BLANK_ [2] Ans: b) _BLANK_ [3]
      • #percentageofapercentage

        (part a):

        Percentage of female

        100% - 60% = 40%

        20% of the female left in the afternoon, so the percentage of people who left

        `20/100` `xx` 40% = 8%

        (part b):

        60% of people - 33 of male = 75% of people

        `->` 60u - 33 = 75% of people

        40% - 8% - 35 of female = 25% of people

        32% of people - 35 of female = 25% of female

        `->` 32u - 35 = 25% of people

        96u - 105 = 75% of people

        60u - 33 = 96u - 105

        105 - 33 = 96u - 60u

        36u = 72

        1u = 72 `-:` 36 = 2

        1u = 1%

        100u = 2 `xx` 100 = 200