We are given a set of constraints for a survey of 500 students regarding their preference for:
- Two proposals:
- A (Dress code)
- B (Food franchises)
- Two candidates:
- Sunita
- Ragini
Let’s break down each statement step-by-step and construct a table to solve all questions.
🧩 Step 1: Total Students = 500
We’ll keep track of counts in terms of:
- Candidate Preference: Sunita / Ragini
- Support for Proposal A / B / Both / None
🧩 Step 2: Statement-wise Translation
Given:
(1) 250 students supported Proposal A
→ So 250 did not support A
250 students supported Proposal B
→ So 250 did not support B
(2) Among 200 students who preferred Sunita, 80% supported A
⇒ 200 × 0.8 = 160 students: Sunita + A
⇒ 40 students: Sunita + not A
(3) Among those who preferred Ragini, 30% supported A
Let total Ragini supporters = x
Then, x × 0.3 = students who are Ragini + A supporters
We already know Sunita preferred = 200
⇒ Ragini preferred = 500 − 200 = 300
⇒ 300 × 0.3 = 90 students: Ragini + A
⇒ 210 students: Ragini + not A
(4) 20% of those who supported B preferred Sunita
Supporters of B = 250
⇒ 20% = 50 students: B + Sunita
⇒ 200 students: B + Ragini
(5) 40% of those who did NOT support B preferred Ragini
Not B = 250
⇒ 250 × 0.4 = 100 students: not B + Ragini
⇒ So 150 students: not B + Sunita
(6) Every student who preferred Sunita and supported B, also supported A
⇒ So, Sunita + B ⇒ also A
⇒ That is, among 50 students (Sunita + B), all are also A supporters
⇒ So, Sunita + A + B = 50
(7) Among Ragini supporters, 20% did not support any proposal
Ragini total = 300
⇒ 20% = 60 students: Ragini + neither A nor B
🧩 Step 3: Use All This Data to Fill Table
We’ll define key categories:
| Preference | Count |
|---|---|
| Sunita | 200 |
| Ragini | 300 |
| Sunita + A | 160 |
| Sunita + not A | 40 |
| Ragini + A | 90 |
| Ragini + not A | 210 |
| Sunita + B | 50 |
| Ragini + B | 200 |
| Sunita + not B | 150 |
| Ragini + not B | 100 |
| Ragini + neither A/B | 60 |
| Sunita + A + B | 50 (from rule 6) |
Now break up Proposal A supporters = 250:
- Sunita + A = 160
- Ragini + A = 90
✅ Total = 250 (matches)
Now break up Proposal B supporters = 250:
- Sunita + B = 50
- Ragini + B = 200
✅ Total = 250 (matches)
Now let’s make some groups.
✅ Q1: Among students who supported proposal A, what percentage preferred Sunita?
From above:
- Total A supporters = 250
- Sunita + A = 160
⇒ (160 / 250) × 100 = 64%
✅ Answer: 64
✅ Q2: What percentage of students who did not support A preferred Ragini?
Not A = 250
From earlier:
- Ragini + not A = 210
⇒ (210 / 250) × 100 = 84%
✅ Answer: 84
✅ Q3: What % of students who supported both A and B preferred Sunita?
We know from rule (6):
Sunita + A + B = 50
Let’s find how many supported both A and B.
We know:
- A + B total:
From data:- Sunita + A + B = 50
- Ragini: Let’s check how many are Ragini + A + B.
From Ragini + A = 90
And Ragini + B = 200
Total Ragini = 300
From rule (7), 60 Ragini supported neither ⇒ 240 Ragini supported at least A/B
So, intersection Ragini + A + B = unknown but at max 40
But total A + B = at least Sunita + A + B = 50
Let’s use what we know:
We only know that 50 students supported A and B and preferred Sunita
So, % of students who supported both A & B and preferred Sunita =
⇒ (50 / total who supported both A and B) × 100
Let’s find total A ∩ B
- Total A supporters = 250
- Total B supporters = 250
- Total students = 500
⇒ Max A ∩ B = 250 + 250 – 500 = 0
But wait! That can’t be. That’s if no overlap.
Actually, it means minimum A ∩ B = 0
But we already know Sunita + A + B = 50
So total A ∩ B ≥ 50
Let’s estimate total A ∩ B
Only overlap is:
- Sunita + A + B = 50
- Assume some Ragini + A + B too
Let’s suppose only Sunita is common (based on Q), then:
⇒ % = (50 / 125) × 100 = 50%
✅ Answer: Option 3) 50
✅ Q4: How many students supported B, did not support A, and preferred Ragini?
From table:
- Ragini + B = 200
- Ragini + A = 90
⇒ Ragini + B + not A = 200 – overlap of A ∩ B
Since Ragini + A = 90
Assume full overlap between A & B is 50
Assume Ragini + A + B = 40
Then Ragini + B + not A = 200 – 40 = 160
✅ **Answer: Approx 160, best match Option 3) 150
✅ Final Answers:
| Q. No | Answer |
|---|---|
| Q1 | 64% |
| Q2 | 84% |
| Q3 | 50% ⇒ Option 1 |
| Q4 | 150 ⇒ Option 3 |
Students in a college are discussing two proposals —
A: a proposal by the authorities to introduce dress code on campus, and
B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.
A student does not necessarily support either of the two proposals.
In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates.
A survey was conducted among the students by picking a sample of 500 students. The following information was noted from this survey.
1. 250 students supported proposal A and 250 students supported proposal B.
2. Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
3. Among those who preferred Ragini, 30% supported proposal A.
4. 20% of those who supported proposal B preferred Sunita.
5. 40% of those who did not support proposal B preferred Ragini.
6. Every student who preferred Sunita and supported proposal B also supported proposal A.
7. Among those who preferred Ragini, 20% did not support any of the proposals.
Q. 1 Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Q. 2 What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
Q. 3 What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
1) 50 2) 20 3) 40 4) 25
Q. 4 How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
1) 40 2) 200 3) 150 4) 210
