The people eating in a certain cafeteria are either faculty members or

Question

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

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

jrk23 · Answer

C 1/2

85 students +15 faculty =100

Students left and remaining total is 50

X+15=50

So x is 35
Number of students left is 85-35=50

50/100 =1/2

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techiesam · Answer

+1 D

Assume,

Total number of Faculty=F
Total number of Students=S
After some students left,New number of students=S1

Now,
we get F=.15(F+S)----(1)
--> F=3/17S

Now After some of the students left, the total number of persons remaining is 50 percent of the original total

i.e, F+S1=.5(F+S)---(2)

Solving 1 and 2 we get

S1=7/17 S

Hence, answer is D.

surbhipuri · Answer

Let x be the total number of people.therefore number of faculty =0.15x 
No of students =0.85x
Let students who left be y then 
0.15x+0.85x -y=0.5x
solving we get
x=2y
y/x=1/2
Please let me know if i m wrong somewhere

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jrk23 · Answer

Sorry 50/85 question is asking students left to original students...

So 10/17 answer is B

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surbhipuri · Answer

Sorry didnt readthe question properly i guess
Student left / total students
=x/2×0.85x
=10/17
Is the answer

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jrk23 · Answer

You should not use x in denominator, you should use .85x in denominator

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surbhipuri · Answer

Corrected the same sir

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CharuSingh26 · Answer

let The Total no of students =100
then no of faculty = 15
no of student =85
let p no of student left
so , 100-p=50*100/100
p=50 students left
so, No of student left /total no of student = 35/85=7/17

CharuSingh26 · Answer

let The Total no of students =100
then no of faculty = 15
no of student =85
let p no of student left
so , 100-p=50*100/100
p=50 students left
so, No of student left /total no of student = 50/85=10/17

surbhipuri · Answer

No of student left is 50 as you calculated
So answer should be 50/85=10/17

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CanCanuck90 · Answer

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

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

Answer is B.  
Picking smart numbers start with 85 students and 15 teachers. After some students leave there is half as many people, meaning 50 students have left.
50/85 = 10/17 when simplified.

IdiomSavant · Answer

50 students do not leave. 50 people leave. 
Your scenario has to go from 15/100 people are teachers to 15/50 teachers.
This means you go from 85 students to 35 students.

D. 7/17

It also easier if you pick 30/200 teachers and then after kids leave its 30/100 teachers. 170 students down to 70 students. 70/170 =7/17

CanCanuck90 · Answer

Re-read the question, it says "after some students leave".... I agree with everything else.

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ScottTargetTestPrep · Answer

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:

/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

techiesam · Answer

Sorry guys...the answer should be B
I did the calculation right but didnot read the question properly.
The question asks (S-S1)/S=?
ITS 10/17.
So its B

nitinthampy123 · Answer

Let total number of people in cafteria be 100.

Given - 15% of total are faculty members - 15
 85 % would be students - 85
 
2 ] After some students leave the total number of people becomes 50% of what was at the start - 50% of 100 - 50
 Number of students who left = 50 - 15 = 35

The number of students who left is what fractional part of the original number of students = 35/85 = 7/17.

OC2910 · Answer

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)

ramblers · Answer

Really nice trap in answer C (students to overall total, not original students.)

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