Ratio of Boys vĩ đại Girls who participate in SSC = 4 : 3
Ratio of Boys vĩ đại Girls who participate in PO = 8 : 13
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Ratio of Boy vĩ đại Girl who participates in both the events of PO and SSC = 2 : 1
Ratio of Boys vĩ đại Girls who participate only in the PO sự kiện = 1 : 2
participation of boys in the SSC sự kiện alone is 10 more than vãn the Girls participation in PO alone
Boys who participate in both SSC and PO is 20% of the Boys who participate in Dancing events alone
Concept:
Total participant in SSC = participate only in SSC + participate in both SSC and PO
Total participant in PO = participate only in PO + participate in both SSC and PO
Total participant in competition = participate only in SSC + participate in both SSC and PO + participate only in PO
Calculation:
Let number of Girl participate only in SSC = x
So, Number of Boys participate only in SSC = x + 10
Number of Boys participate in both SSC and PO = (20/100) × (x + 10)
⇒ (x + 10)/5
Number of Girls participate in both SSC and PO = (1/2) × {(x + 10)/5}
⇒ (x + 10)/10
Number of Boys participate in SSC/Number of girls participate in SSC = 4/3
4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}
⇒ 2/3 = (6x + 60)/(11x + 10)
⇒ 18x + 180 = 22x + 20
⇒ 4x = 160
⇒ x = 40
Number of Girl participate only in SSC = 40
Number of Boys participate only in SSC = 40 + 10
⇒ 50
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Number of Boys participate in both SSC and PO = (40 + 10)/5
⇒ 10
Number of Girls participate in both SSC PO= (40 + 10)/10
⇒ 5
Number of Boys participate in SSC = 50 + 10
⇒ 60
Number of girls participate in SSC = 40 + 5
⇒ 45
Number of Boys in PO/Number of Girls in PO = 8/13
8/13 = (10 + y)/(5 + 2y)
⇒ 40 + 16y = 130 + 13y
⇒ 3y = 90
⇒ hắn = 30
Number of Boys in PO only = 30
Number of Girls in PO only = 2 × 30
⇒ 60
Number of Boys in PO = 30 + 10
⇒ 40
Number of Girls in PO = 60 + 5
⇒ 65
Total participant in competition = (50 + 40) +(10 + 5) + (30 + 60)
⇒ 90 + 15 + 90
⇒ 195
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∴ Total 195 participants were there in the competition.
Last updated on Mar 24, 2023
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