Question

Comprehension

Instructions: Study the following information carefully and answer accordingly.

In the SSC and PO exams, among a certain number of participants (Boy + Girl), some participate in both the events of SSC and PO while some of them participate in PO or SSC alone.

The ratio of Boys to Girls who participate in SSC and PO is 4 : 3 and 8 : 13 respectively, while the ratio of Boy to Girl who participates in both the exams PO and SSC is 2 : 1 and the ratio of Boys to Girls who participate only in the PO exams is  1 : 2. The participation of boys in the SSC exam alone is 10 more than the Girls who participate in it. Boys who participate in both SSC and PO is 20% of the Boys who participate in SSC events alone.

How many participants were there in the competition?

1. 190
2. 199
3. 250
4. 195
5. 205

Answer 1

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.