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At Brightwell Logistics, the 30 employees in the warehouse department earn an average salary of $50,000, and the employees in the dispatch department earn an average salary of $70,000. The average salary across both departments combined is $62,000. How many employees are in the dispatch department?
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Correct answer
C
Let d be the number of dispatch employees. Weighting each department average by its headcount: (30 × 50,000 + d × 70,000) / (30 + d) = 62,000. Then 1,500,000 + 70,000d = 1,860,000 + 62,000d, so 8,000d = 360,000 and d = 45.
By alligation, the combined average $62,000 lies $12,000 above warehouse and $8,000 below dispatch, so warehouse-to-dispatch headcount = 8 to 12 = 2 to 3, giving dispatch = 30 × 3/2 = 45.
The most tempting wrong answer is (A) 20: inverting the alligation ratio yields 30 × 8/12 = 20. The combined average sits closer to dispatch's $70,000, so dispatch must be the larger group, confirming 45 over 20.
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