Instructions

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.

Question 30.

What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?

A
B
C
D

Question Explanation

Text Explanation

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 percentage of the students surveyed who did not support proposal A preferred Ragini as student union president = 210/250=84%

Answer 84 

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