Aman verma wrote:Q: The average salary paid to all its employees by Mckinsey & Co. is $ 15500. The average salary of the senior employees is $ 18000 per month and the average salary of junior employees is $ 12000 per month. If there are only two levels of employees viz. junior and senior level, then what fraction of the total employees is the junior level employees ?
A) 7/10
B) 5/12
C) 5/16
D) 7/16
E) 7/12
This is a WEIGHTED AVERAGE/MIXTURE problem.
Let S = senior employees and J = junior employees.
Average salary for S = 18000.
Average salary for J = 12000.
Average salary for the MIXTURE of S+J = 15500.
To determine the ratio of S to J in the mixture, use ALLIGATION.
Step 1: Plot the 3 averages on a number line, with the averages for S and J on the ends and the average for the mixture in the middle.
S 18000---------------15500--------------12000 J
Step 2: Calculate the distances between the averages.
S 18000-----
2500-----15500-----
3500-----12000 J
Step 3: Determine the ratio in the mixture.
The required ratio of S to J is equal to the RECIPROCAL of the distances in red:
S:J = 3500:2500 = 7:5.
Since S=7 and J=5, of every 12 employees, 7 are senior and 5 are junior.
Thus, junior/total = 5/12.
The correct answer is
B.
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