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For each month of a given year except December

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For each month of a given year except December [#permalink]

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For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?

A) 8/5

B) 5/2

C) 3

D) 11/3

E) 4
[Reveal] Spoiler: OA

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shapla wrote:
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?

A) 8/5

B) 5/2

C) 3

D) 11/3

E) 4


Let monthly salary for each of the 11 months except December was x, then

11x*1/10 + Nx*1/5 = 1/8(11x + Nx);

11/10 + N/5 = 1/8(11 + N)

N = 11/3.

Answer: D.
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Re: For each month of a given year except December [#permalink]

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New post 12 Mar 2016, 17:12
Salary = s
Donation for 11 months = 1/10 ( 11*s)
Donation for December = 1/5 (N*s)
Total Donation = 11s/10+ Ns/5 = ( 11s+2Ns)/10 = s(11+2N)/10

Total Salary = 11*2+N+s = s (11+N)
Total Donation = s(11+N)/8

--> set both donation equations equal to each other:
1. s(11+N)/8 = s(11+2N)/10
2. cancel "s" on both sides
3. 10 (11+N) = 8 (11+2N) = 110 N + 10 N = 88 + 16N
4. N = 22 / 6 = 11/3
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For each month of a given year except December [#permalink]

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New post 12 Mar 2016, 19:40
Expert's post
shapla wrote:
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?

A) 8/5

B) 5/2

C) 3

D) 11/3

E) 4


Hi,
Apart from the method of [b]Bunuel, we can do it by weighted average method, by taking this too as MIXTURE.
so the quantities are
1) 11 units of 1/10
2) N units of 1/5
average= 1/8 of (N+11)[/b]

so\({(\frac{1}{8}-\frac{1}{10})}/{(\frac{1}{5}-\frac{1}{10})}=\frac{N}{(N+11)}\)..
\({\frac{1}{40}/\frac{1}{10}}=\frac{N}{(N+11)}\)..
\(\frac{1}{4}=\frac{N}{(N+11)}\)
N+11=4N..
3N=11..
N=11/3
D
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Re: For each month of a given year except December [#permalink]

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New post 13 Mar 2016, 04:26
shapla wrote:
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?

A) 8/5

B) 5/2

C) 3

D) 11/3

E) 4


Supposing that worker's monthly salary is $10 per month, he earns $110 and gives charity $11 for 11 months.
In December he earns 10*N and gives charity 2*N
Total salary 110+10*N
Charity 11+2*N
By supposition,
88+16*N = 110+10*N
Solving N = 11/3
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For each month of a given year except December, a worker earned the [#permalink]

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New post 24 Jul 2016, 11:26
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?


A) 8/5
B) 5/2
C) 3
D) 11/3
E) 4
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Re: For each month of a given year except December [#permalink]

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New post 24 Jul 2016, 11:32
Expert's post
Avigano wrote:
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-eighth of his earnings for the entire year, what is the value of N?


A) 8/5
B) 5/2
C) 3
D) 11/3
E) 4


Merging topics. Please refer to the discussion above.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: For each month of a given year except December [#permalink]

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New post 21 Mar 2018, 13:11
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Re: For each month of a given year except December   [#permalink] 21 Mar 2018, 13:11
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