Directions: Study the following information carefully and answer acco...
Given
Ratio of Boys to Girls who participate in Dancing = 4 : 3
Ratio of Boys to Girls who participate in Singing = 8 : 13
Ratio of Boy to Girl who participates in both the events of Singing and Dancing = 2 : 1
Ratio of Boys to Girls who participate only in the Singing event = 1 : 2
Participation of boys in the Dancing event alone is 10 more than the Girls participation in Dancing alone
Boys who participate in both Dancing and Singing is 20% of the Boys who participate in Dancing events alone
Concept:
Total participant in Dance = Participate only in Dance + Participate in both Dancing and Singing
Total participant in Singing = Participate only in Singing + Participate in both Dancing and Singing
Total participant in competition = Participate only in Dance + Participate in both Dancing and Singing + Participate only in Singing
Let the number of Girl participate only in dancing = x
So, the Number of Boys participate only in dancing = x + 10
Number of Boys participate in both Dancing and Singing = (20/100) x (x + 10)
⇒ (x+10)/5
Number of Girls participate in both Dancing and Singing =
⇒ 18x + 180 = 22x + 20
⇒ 4x = 160
⇒ x = 40
Number of Girl participate only in dancing = 40
Number of Boys participate only in dancing = 40 + 10 ⇒ 50
Number of Boys participate in both Dancing and Singing = (40+10)/5 ⇒ 10
Number of Girls participate in both Dancing and Singing = (40+10)/10 ⇒ 5
Number of Boys participate in dance = 50 + 10 ⇒ 60
Number of girls participate in dance = 40 + 5 ⇒ 45
Number of Boys in singing/Number of Girls in singing = 8/13
⇒ 40 + 16y = 130 + 13y
⇒ 3y = 90
⇒ y = 30
Number of Boys in singing only = 30
Number of Girls in singing only = 2 × 30 ⇒ 60
Participant only in Dancing = 50 + 40 ⇒ 90
Participant only in Singing = 30 + 60 ⇒ 90
Participant only in Dancing : Participant only in Singing = 90 : 90 ⇒ 1 : 1
∴ Ratio of participants who participated only in Dancing to only in Singing is 1 : 1.
Hence, the correct option is (A).