Correct Answer - Option 4 : 195

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 event alone is 10 more than 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

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

⇒ y = 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

**∴ Total 195 ****participants were there in the competition.**