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Bunuel
The people eating in a certain cafeteria are either faculty members or students, and the number of faculty members is 15 percent of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50 percent of the original total. The number of students who left is what fractional part of the original number of students?

(A) 17/20
(B) 10/17
(C) 1/2
(D) 7/17
(E) 7/20

If we let the total people = n, then 0.15n = faculty and 0.85n = students. If we let x = the number of students who leave, we can create the equation:

[0.15n + (0.85n - x)]/n = 1/2

(n - x)/n = 1/2

2(n - x) = n

2n - 2x = n

n = 2x

n/2 = x

Thus, the number of students who left is (n/2)/(85n/100) = 100n/170n = 10/17 of the original number of students.

Answer: B
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this question definitely calls for test it
so draw a table
total student teachers
100 85 15 ........as 15 percent are teacher
50 35 15 ............ as total number reduce to half but teachers are same so only students reduce

required ratio = no of students left/total no of students =85-35/85=50/85=10/17 (B)
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Really nice trap in answer C (students to overall total, not original students.)
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15% is 3/20, so suppose there were 3 faculty members and 17 students, 20 people in total. If half the people remain , 10 of the 17 students have left .
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