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At a certain high school, the student to teacher ratio is 25:1. If the

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At a certain high school, the student to teacher ratio is 25:1. If the  [#permalink]

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New post 29 Aug 2017, 23:43
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At a certain high school, the student to teacher ratio is 25:1. If the number of students increases by 50% and 10% of teachers are laid off, what would be the new student to teacher ratio? (Assume that no other changes happen)

A. 40:1
B. 125:3
C. 75:2
D. 145:9
E. Cannot be determined

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At a certain high school, the student to teacher ratio is 25:1. If the  [#permalink]

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New post Updated on: 30 Aug 2017, 00:31
Bunuel wrote:
At a certain high school, the student to teacher ratio is 25:1. If the number of students increases by 50% and 10% of teachers are laid off, what would be the new student to teacher ratio? (Assume that no other changes happen)

A. 40:1
B. 125:3
C. 75:2
D. 145:9
E. Cannot be determined



Ratio of student:teacher = 25:1 Let common Factor be x. So no of students:Tecaher will be 25x:1x

Now Number of students = 25x+(50%*25x) = 75x/2
Number of teachers = x-(10x/100)=9x/10

Student:Teacher Ratio will be (75x/2)/(9x/10) = 125:3

Hence answer is B.

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Originally posted by kill3rlook5 on 30 Aug 2017, 00:22.
Last edited by kill3rlook5 on 30 Aug 2017, 00:31, edited 1 time in total.
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Re: At a certain high school, the student to teacher ratio is 25:1. If the  [#permalink]

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New post 30 Aug 2017, 00:30
Bunuel wrote:
At a certain high school, the student to teacher ratio is 25:1. If the number of students increases by 50% and 10% of teachers are laid off, what would be the new student to teacher ratio? (Assume that no other changes happen)

A. 40:1
B. 125:3
C. 75:2
D. 145:9
E. Cannot be determined


2500:100
3750:90
375:9
125:3

250:10
375:9
125:3

500:20
750:18
125:3

B
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Re: At a certain high school, the student to teacher ratio is 25:1. If the  [#permalink]

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New post 30 Aug 2017, 00:37
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Bunuel wrote:
At a certain high school, the student to teacher ratio is 25:1. If the number of students increases by 50% and 10% of teachers are laid off, what would be the new student to teacher ratio? (Assume that no other changes happen)

A. 40:1
B. 125:3
C. 75:2
D. 145:9
E. Cannot be determined


- 10% teacher is the key. We should plug in the value that give the integer for 10% of teacher.
- Let say number of teacher = 10 (10 times the ratio), so the number of stundent = 25*10 = 250.
- Students increase 50% -> \(250*1.5\) = 375 students
- Teacher laid off 10% -> \(10*0.9\)= 9 teachers.
- New ration = \(\frac{375}{9}\), divide by 3 = \(\frac{125}{3}\)

B.
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Re: At a certain high school, the student to teacher ratio is 25:1. If the  [#permalink]

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New post 02 Sep 2017, 07:16
Bunuel wrote:
At a certain high school, the student to teacher ratio is 25:1. If the number of students increases by 50% and 10% of teachers are laid off, what would be the new student to teacher ratio? (Assume that no other changes happen)

A. 40:1
B. 125:3
C. 75:2
D. 145:9
E. Cannot be determined


We have a current ratio of 25/1 = students to teachers. After 50% more students arrive and 10% of the teachers are laid off, we have:

25(1.5)/0.9 = 37.5/0.9 = 375/9 = 125/3

Alternate Solution:

Let’s say there were 250 students and 10 teachers. After 50% more students arrive, there will be 250 + 125 = 375 students. After 10% of the teachers are laid off, there will be 10 - 1 = 9 teachers. Thus, the new ratio will be 375/9 = 125/3.

Answer: B
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Re: At a certain high school, the student to teacher ratio is 25:1. If the   [#permalink] 02 Sep 2017, 07:16
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