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Question:

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

Explanation:

	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.