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.
Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Correct Answer: 64
Total number of students surveyed= 500
Every student prefers one of the two candidates. Ragini(R) and Sunita(S).
Thus, R+S=500.
According to statement 2, "Among the 200 students who preferred Sunita as student union president, 80% supported proposal A."
The number of students who support Sunita(S)=200
The number of students who supported Ragini(R)=300
According to statements 2 and 3, 160 students who supported Sunita also supported the proposal A & 90 students who supported Ragini also supported proposal A.
According to statements 4 and 6, we can make the following Venn diagram for Sunita.
According to statement 5 and 7, we can make the following Venn diagram.
The number of students who preferred Sunita and the proposal A=160
=160/250= 64%
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