swerve wrote:Last year at an accounting firm, accountants made up 40% of the total employees. This year, 50% of these accountants left for another company, and new accountants, which amounts to 50% of the total employees left, joined the company. What percent of the total employees are accountants this year?
A. 10%
B. 20%
C. 25%
D. 30%
E. 50%
The OA is E.
I need help with this PS question. Please, can any expert assist me with it? Thanks.
We can let the total number of employees = E. Thus, the number of accountants is 0.4E.
We are given that this year, 50% of these accountants left for another company, so 0.5(0.4E) = 0.2E of the accountants left for another company. Thus, there are 0.8E left at the company.
Now, since the number of new accountants who joined the company amounts to 50% of the total employees left, the number of new accountants added to the company is 0.5(0.8E) = 0.4E.
Thus, this year we have a total of 0.4E - 0.2E + 0.4E = 0.6E accountants and a total of E - 0.2E + 0.4E = 1.2E employees. So the percent of the total employees who are accountants this year is:
0.6E/1.2E = 0.6/1.2 = 1/2 = 50%
Alternate Solution:
Let's let 100 = the number of employees last year. Thus, 40 of them were accountants last year. This year, 50% of the accountants (20 accountants) left, and thus, there were 80 employees left (including 20 accountants). New accountants were hired, and they constituted half of those 80 remaining employees, so the number of accountants hired is 40. So now, there are 80 + 40 = 120 employees, and the number of accountants is 20 + 40 = 60 accountants. Thus, this year, the percent of accountants is 6/120 = 0.5 = 50%.
Answer: E
