AAPL wrote:Manhattan Prep

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

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

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

$$11x*\frac{1}{10}+Nx*\frac{1}{5}=\frac{1}{8}(11x+Nx);$$
$$\frac{11}{10}+\frac{N}{5}=\frac{1}{8}(11+N)$$
$$N=\frac{11}{13}$$

Hence, D is the correct answer.