Correct Answer - Option 4 : 15
Ratio of Boys to Girls who participate in SSC = 4 : 3
Ratio of Boys to Girls who participate in PO = 8 : 13
Ratio of Boy to Girl who participates in both the events of PO and SSC = 2 : 1
Ratio of Boys to Girls who participate only in the PO event = 1 : 2
participation of boys in the SSC exam alone is 10 more than the Girls participation in SSC alone
Boys who participate in both SSC and PO is 20% of the Boys who participate in SSC exam 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
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
Number of Boys participate in both SSC and PO = (40 + 10)/5
⇒ 10
Number of Girls participate in both SSC and PO = (40 + 10)/10
⇒ 5
number of participants who participated in both events (SSC and PO) = 10 + 5
⇒ 15
∴ 15 participants, participated in both exams (SSC and PO).