Logical Reasoning – Students in a college are discussing two proposals


Slot – 2 – LR

Students in a college are discussing two proposals – Video Solution


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?

Answer: 64

Q.2 What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?

Answer: 84

Q.3 What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?

  1. 25
  2. 40
  3. 20
  4. 50
Answer: 4

Q.4 How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?

  1. 150
  2. 40
  3. 200
  4. 210
Answer: 1

Solution:
As per question it is clear that a student can not prefer both Ragini and Sunita simultaneously. So on the basis of information given , table can be formed as given below:
  Sunita Ragini Total
A     250
B     250
Both A and B      
None      
Total     500

Now from point 2 it is clear that 200 students preferred Sunita so no of students who preferred Ragini = 500 – 200 = 300
No of students who preferred Sunita and supported proposal A = 80% of 200 = 160
From point 3) , no of students who preferred Ragini and supported proposal A = 30% of 300 = 90
From point 4) No of students who preferred Sunita and supported proposal B = 20% of 250 = 50
From point 6) No of students who preferred Sunita and supported proposal A and B both = 50
From point 7) no of students who preferred Ragini and didn’t supported any proposal = 20% of 300 = 60
Now the complete table can be formed as given below:
  Sunita Ragini Total
A 160 90 250
B 50 200 250
Both A and B 50 50 100
None 40 60 100
Total 200 300 500

  1. No of surveyed who supported proposal A, percentage of students who Preferred Sunita for student union president = 160/250 *100 = 64%
  2. No of the students surveyed who did not support proposal A Preferred Ragini as student union president = 300 – 90 = 210
    Required percentage = 210/250*100 = 84%
  3. No of students who supported both proposals = 100
    No of the students surveyed who supported both proposals A and B and Preferred Sunita as student union president = 50
    Thus required % tage = 50/100 *100 = 50 %
  4. No of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president
    = no of students who supported proposal B and preferred Ragini – no of students who supported proposal A and B and preferred Ragini
    = 200 – 50 = 150


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