CAT 2019 Slot 2 — DILR Question 27
Answer the following questions based on the information given below.
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.
- 250 students supported proposal A and 250 students supported proposal B.
- Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
- Among those who preferred Ragini, 30% supported proposal A.
- 20% of those who supported proposal B preferred Sunita.
- 40% of those who did not support proposal B preferred Ragini.
- Every student who preferred Sunita and supported proposal B also supported proposal A.
- Among those who preferred Ragini, 20% did not support any of the proposals.
What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
Answer & solution
Answer: 84
| Sunita | Ragini | |
| Only proposal A | k | p |
| Only proposal B | l | q |
| Both A and B | m | r |
| Neither A nor B | n | s |
From (1), k + m + p + r = 250 and l + m + q + r = 250
From (4), l + m = 0.2 × 250 = 50
From (6), l = 0 ⇒ m = 50
∴ q + r = 200
From (2), k + l + m + n = 200 and hence p + q + r + s = 300
From (3), p + r = 0.3 × 300 = 90 ⇒ k + m = 160
As l = 0 and k + l + m + n = 200, n = 40
∴ k = 110
From (7), n + s = 100 ⇒ s = 60
∴ p + q + r = 240 and p + r = 90 ⇒ q = 150
∴ q + r = 200 ⇒ r = 50 and hence p = 40
Thus, we have
| Sunita | Ragini | |
| Only proposal A | 110 | 40 |
| Only proposal B | 0 | 150 |
| Both A and B | 50 | 50 |
| Neither A nor B | 40 | 60 |
250 students did not support proposal A. Out of these, 150 + 60 = 210 students preferred Ragini as student union president, which is equivalent to 84%.
Answer: 84.