Night reader wrote:Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. The two companies merge, every employee stays with the resulting company, and no new employees are added. If the resulting company's workforce consists of 25 percent managers, what percent of the workforce originated from Company A?
(A) 10%
(B) 20%
(C) 25%
(D) 50%
(E) 75%
This is a weighted average question. Company A is 10% managers. Company B is 30% managers. We want to combine the two companies so that the resulting combination is 25% managers. A great method for solving is called
alligation.
To combine a 10% entity with a 30% entity to get a combined entity that is 25%:
The proportion needed of each starting percentage is the positive difference between the other 2 percentages.
Proportion needed of the 10% entity = 30-25 = 5.
Proportion needed of the 30% entity = 25-10 = 15.
Thus, Company A: Company B = 5:15 = 1:3.
Thus, 1/4 = 25% of the combined entity must come from Company A.
The correct answer is
C.
Another approach would be to plug in the answer choices, which represent the percentage of the merged company that must come from company A.
Answer choice C: 25% from Company A
Plug in A = 100 employees.
Plug in B = 300 employees.
10% of A = 10 managers.
30% of B = 90 managers.
Total managers = 10+90 = 100.
Total employees = 100+300 = 400.
Managers/employees = 100/400 = 25%. Success!
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