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A company has only two types of employees - clerks and managers. The a

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A company has only two types of employees - clerks and managers. The a [#permalink] New post   21 Feb 2021, 08:17
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A company has only two types of employees - clerks and managers. The average salary of the clerks is $40,000 and the average salary of the managers is $120,000. If the average salary of all employees in the company is $45,000 and there are 30 managers in the company, what is the number of clerks in the company?

(A) 2
(B) 20
(C) 45
(D) 200
(E) 450
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E
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A company has only two types of employees - clerks and managers. The a [#permalink] New post   21 Feb 2021, 10:37
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Clerks get $40 and managers get $120
Average is $45

Deviation from mean for each manager = (+)$75
For 30 managers, total positive deviation = 30 * 75 = 2250

Deviation from mean for clerks = (-)$5

Since sum of deviations about mean MUST be ZERO, we have:

Total negative deviation for clerks = -2250
Thus, number of clerks = (-2250)/(-5) = 450

Answer E

Posted from my mobile device


Alternatively, you may form an equation assuming x clerks and solve for x (the longer way)
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Re: A company has only two types of employees - clerks and managers. The a [#permalink] New post   27 Feb 2021, 03:06
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Clerks get 40 and Managers 120
There is 30 managers
x is the number of Clerks in the company

Use the average method:
(30*120+x*40)/(30+x) = 45

3600+40x = 1350 + 45x
x=2250/5
x= 450

Hence answer E
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Re: A company has only two types of employees - clerks and managers. The a [#permalink] New post   28 Feb 2021, 08:25
Expert Reply
Given
    • A company has only two types of employees - clerks and managers.
    • Average salary of the clerks = $40,000
    • Average salary of the Manager = $120,000
    • Average salary of all employees in the company = $45,000
    • Total managers in the company = 30
To find

    • Number of clerks in the company

Approach
Let number of clerks in the company = n
    • Total Salary of Managers + Total salary of clerks = Total salary paid to all employees
    • 30 × $120,000 + n × $40,000 = (30 + n) × $45,000
    • 30 × 24 + n × 8 = (30 + n) × 9
    • n = 30 × 15
    • n = 450

Hence, the correct answer is option E.
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Re: A company has only two types of employees - clerks and managers. The a [#permalink] New post   28 Feb 2021, 19:11
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Use the rule of alligations as shown below.

Let x be the number of clerks

Therefore \(\frac{x}{75000} = \frac{30}{5000}\)

x = 450


Option E

Arun Kumar
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Re: A company has only two types of employees - clerks and managers. The a [#permalink] New post   04 Mar 2021, 14:09
Camcam1 wrote:
Clerks get 40 and Managers 120
There is 30 managers
x is the number of Clerks in the company

Use the average method:
(30*120+x*40)/(30+x) = 45

3600+40x = 1350 + 45x
x=2250/5
x= 450

Hence answer E

How long did this take you? I solved this way and took just under 3 min :cry:
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Re: A company has only two types of employees - clerks and managers. The a [#permalink] New post   02 Jun 2023, 23:17
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