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?
195
Solving Participant Count in SSC and PO Exams
The problem asks us to find the total number of participants (Boys + Girls) in a competition involving SSC and PO exams, based on given ratios and conditions regarding participation in only one exam or both.
Breaking Down the Problem
The participants are divided into categories:
- Those who participate only in SSC.
- Those who participate only in PO.
- Those who participate in both SSC and PO.
Within each category, there are boys and girls.
Defining Variables
Let's use variables to represent the number of participants in each sub-category:
- B_SSC_only: Number of boys participating only in SSC.
- G_SSC_only: Number of girls participating only in SSC.
- B_PO_only: Number of boys participating only in PO.
- G_PO_only: Number of girls participating only in PO.
- B_Both: Number of boys participating in both SSC and PO.
- G_Both: Number of girls participating in both SSC and PO.
Using the Given Information
We are given the following relationships:
- Ratio of Boys : Girls in Both = 2 : 1. Let G_Both =
x. Then B_Both =2x. - Ratio of Boys : Girls in Only PO = 1 : 2. Let B_PO_only =
y. Then G_PO_only =2y. - Boys Only SSC = Girls Only SSC + 10. Let G_SSC_only =
z. Then B_SSC_only =z + 10. - Boys in Both = 20% of Boys Only SSC. This means
B_Both = 0.20 × B_SSC_only. - Ratio of Total Boys : Total Girls in SSC = 4 : 3. Total Boys in SSC = B_SSC_only + B_Both. Total Girls in SSC = G_SSC_only + G_Both.
- Ratio of Total Boys : Total Girls in PO = 8 : 13. Total Boys in PO = B_PO_only + B_Both. Total Girls in PO = G_PO_only + G_Both.
Solving for the Variables
From the condition "Boys in Both = 20% of Boys Only SSC":
2x = 0.20 × (z + 10)
2x = 0.2z + 2
x = 0.1z + 1 (Equation 1)
Using the ratio for Total SSC (Boys : Girls = 4 : 3):
(B_SSC_only + B_Both) / (G_SSC_only + G_Both) = 4 / 3
Substitute the variables:
((z + 10) + 2x) / (z + x) = 4 / 3
3 × (z + 10 + 2x) = 4 × (z + x)
3z + 30 + 6x = 4z + 4x
30 + 2x = z (Equation 2)
Now we solve the system of Equation 1 and Equation 2:
Substitute Equation 1 into Equation 2:
30 + 2 × (0.1z + 1) = z
30 + 0.2z + 2 = z
32 + 0.2z = z
32 = z - 0.2z
32 = 0.8z
z = 32 / 0.8 = 40
Now find x using z = 40 in Equation 1:
x = 0.1 × 40 + 1 = 4 + 1 = 5
So far, we have:
- G_SSC_only = z = 40
- B_SSC_only = z + 10 = 40 + 10 = 50
- G_Both = x = 5
- B_Both = 2x = 2 × 5 = 10
Now let's use the ratio for Total PO (Boys : Girls = 8 : 13):
(B_PO_only + B_Both) / (G_PO_only + G_Both) = 8 / 13
Substitute the variables (using y for PO only and the values for Both):
(y + 10) / (2y + 5) = 8 / 13
13 × (y + 10) = 8 × (2y + 5)
13y + 130 = 16y + 40
130 - 40 = 16y - 13y
90 = 3y
y = 90 / 3 = 30
So, for the Only PO category:
- B_PO_only = y = 30
- G_PO_only = 2y = 2 × 30 = 60
Summary of Participant Numbers
Let's list the number of participants in each category:
| Category | Boys | Girls | Total |
|---|---|---|---|
| Only SSC | 50 | 40 | 90 |
| Only PO | 30 | 60 | 90 |
| Both SSC and PO | 10 | 5 | 15 |
Calculating Total Participants
The total number of participants is the sum of all participants across these three unique categories:
Total Participants = (Boys Only SSC + Girls Only SSC) + (Boys Only PO + Girls Only PO) + (Boys Both + Girls Both)
Total Participants = (50 + 40) + (30 + 60) + (10 + 5)
Total Participants = 90 + 90 + 15
Total Participants = 180 + 15
Total Participants = 195
Final Answer
The total number of participants in the competition is 195.
Important Questions from Caselet DI
Study the given table carefully and answer the following question.
The table shows the percentage of students of four departments - Mechanical, Civil, Computer Science and Applied - with each student being in only one department. The table also shows the number of students of these four departments in five different colleges, with the total number of students being 2080.
If the number of students in IIT Bombay is 20% less than the number of students in IIT Madras, then what is the difference between the total number of students who study in the Applied department in these two colleges and that of the students who study in the Civil department in these two colleges?College Students Mechanical Civil Computer Science Applied IIT Delhi 430 - 20% - 10% IIT Kanpur 350 20% - 25% - IIT Bombay - 20% 18% - 32% IIT Madras - - 25% 18% 35% IIT Guwahati 400 20% 22% - 20% How many students like only one vegetable?
A. 60
B. 61
C. 65
D. 71
The difference between the people who like carrot and cauliflower is
A. 6
B. 18
C. 16
D. 4What is the percentage of students that do not like cabbage?
A. 16
B. 32
C. 24
D. 68
What is the monthly electricity bill for a house with m rooms and consuming n units?
