For each month of a given year except December

Question

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

A) 8/5

B) 5/2

C) 3

D) 11/3

E) 4

Bunuel · Accepted Answer

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.

sq01 · Answer

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

chetan2u · Answer

Hi,
Apart from the method of  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)

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

Mathivanan Palraj · Answer

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

Avigano · Answer

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

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

Bunuel · Answer

Merging topics. Please refer to the discussion above.

JeffTargetTestPrep · Answer

We can let the normal salary = k, so his total salary for the first 11 months was 11k. Each month k/10 went to charity, so for the first 11 months, his total charitable contribution was 11k/10.

The December salary was kN, and kN/5 was donated to charity.

Since the worker's charitable contributions totaled one-eighth of his earnings for the entire year:

kN/5 + 11k/10 = (kN + 11k)/8

Multiplying the equation by 40, we have:

8kN + 44k = 5kN + 55k

Dividing the equation by k, we have:

8N + 44 = 5N + 55

3N = 11

N = 11/3

Answer: D

bumpbot · Answer

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For each month of a given year except December

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