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# A certain company has only directors and managers. The company has 300

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Math Expert
Joined: 02 Sep 2009
Posts: 53008
A certain company has only directors and managers. The company has 300  [#permalink]

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20 Jan 2019, 23:13
00:00

Difficulty:

15% (low)

Question Stats:

92% (01:36) correct 8% (02:59) wrong based on 20 sessions

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A certain company has only directors and managers. The company has 300 directors and 200 managers. If the average age of the directors is 42 and the average age of the managers is 38, what is the average age of all the company’s employees?

A 39.8
B 40
C 40.2
D 40.4
E 41

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Director
Joined: 18 Jul 2018
Posts: 675
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: A certain company has only directors and managers. The company has 300  [#permalink]

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21 Jan 2019, 00:32
$$\frac{300*42+200*38}{500}$$ = $$\frac{12600+7600}{500}$$ = 20200/500 = 40.4

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SVP
Joined: 18 Aug 2017
Posts: 1840
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A certain company has only directors and managers. The company has 300  [#permalink]

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21 Jan 2019, 07:01
Bunuel wrote:
A certain company has only directors and managers. The company has 300 directors and 200 managers. If the average age of the directors is 42 and the average age of the managers is 38, what is the average age of all the company’s employees?

A 39.8
B 40
C 40.2
D 40.4
E 41

director total age = 300*42 = 12600
manager total age = 200* 38 = 7600

total age /total popn = 20200/500 = 40.4
IMO D
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Manager
Joined: 15 Feb 2018
Posts: 244
A certain company has only directors and managers. The company has 300  [#permalink]

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26 Jan 2019, 04:45
Weighted average:
(# directors/#employees)·average age of directors + (# managers/#employees)·average age of directors = overall average
$$\frac{300}{500}·42+\frac{200}{500}·38$$

$$\frac{3}{5}·42+\frac{2}{5}·38$$

$$\frac{126}{5}+\frac{76}{5}$$

$$25.2+15.2$$=40.4 D
A certain company has only directors and managers. The company has 300   [#permalink] 26 Jan 2019, 04:45
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