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Schools A and B are in the same town. Annual fee collected by school A

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Schools A and B are in the same town. Annual fee collected by school A  [#permalink]

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New post 04 Feb 2019, 07:36
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Schools A and B are in the same town. Annual fee collected by school A from each student is $6720 which is comprised of basic fee and an additional maintenance fee which is 12% of the basic fee. School B has the same basic fee as school A but its maintenance charge is just 8% of the basic fee. A student studying in school B can save how much more as compared with a student from school A?

A. $120
B. $240
C. $360
D. $540
E. $720
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Re: Schools A and B are in the same town. Annual fee collected by school A  [#permalink]

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New post 04 Feb 2019, 08:39
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akurathi12 wrote:
Schools A and B are in the same town. Annual fee collected by school A from each student is $6720 which is comprised of basic fee and an additional maintenance fee which is 12% of the basic fee. School B has the same basic fee as school A but its maintenance charge is just 8% of the basic fee. A student studying in school B can save how much more as compared with a student from school A?

A. $120
B. $240
C. $360
D. $540
E. $720


Student A
1.12 BF = 6720
BF = 6000

Student B
1.08 BF = 6480

Student A Fee - Student B Fee
240

B
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Re: Schools A and B are in the same town. Annual fee collected by school A  [#permalink]

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New post 04 Feb 2019, 08:40
1
School A costs $6720 = 1F + 12/100F, i.e. 112/100F
F = 6720*(100/112) = 60*100 = 6000

School B costs 1.08F
.01F = 60 so 8*60 = 480, so School B = 6480
6720 - 6480 = 240
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Re: Schools A and B are in the same town. Annual fee collected by school A  [#permalink]

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New post 06 Feb 2019, 19:01
akurathi12 wrote:
Schools A and B are in the same town. Annual fee collected by school A from each student is $6720 which is comprised of basic fee and an additional maintenance fee which is 12% of the basic fee. School B has the same basic fee as school A but its maintenance charge is just 8% of the basic fee. A student studying in school B can save how much more as compared with a student from school A?

A. $120
B. $240
C. $360
D. $540
E. $720



We can let x = the basic fee in school A. Thus, we can create the equation:

x + 0.12x = 6720

1.12x = 6720

x = 6720/1.12

x = 6000

Therefore, the maintenance fee in school A is 0.12(6000) = 720. Therefore, the maintenance fee in school B is 0.08(6000) = 480. Since the two schools’ basic fees are the same, a student saves money only by comparing the maintenance fees. By studying in school B, the student can save 720 - 480 = 240 dollars.

Answer: B
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Re: Schools A and B are in the same town. Annual fee collected by school A  [#permalink]

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New post 06 Feb 2019, 19:10
akurathi12 wrote:
Schools A and B are in the same town. Annual fee collected by school A from each student is $6720 which is comprised of basic fee and an additional maintenance fee which is 12% of the basic fee. School B has the same basic fee as school A but its maintenance charge is just 8% of the basic fee. A student studying in school B can save how much more as compared with a student from school A?

A. $120
B. $240
C. $360
D. $540
E. $720


Short of time..
You are paying 4% less of (6720-something), so answer should be <\(\frac{4}{100}*6720=268\)
Only 240 is possible as C, D and E are more than that..
A is very less, as we are just looking at 4% of an amount closer to (100-12)% of 6720

Proper method ..
Let basic pay be x
\((1+0.12)x=6720.......x=\frac{6720*100}{112}=6000\)
Now basic fee is 6000, so fees at school B = \((1+0.08)*6000=6480\)

Difference = 6720-6480=240$
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: Schools A and B are in the same town. Annual fee collected by school A   [#permalink] 06 Feb 2019, 19:10
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